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TR67 MOVEMENT, RESTRAINT AND CRACKING IN CONCRETE STRUCTURES, 2008 Amendment No.1 May 2008

Page 72, Paragraph 4 Delete: “is presented in Section A.1 in Appendix A.” Substitute: “has been presented by Alexander(39).” Page 75, References Delete: References 39, 40 and 41. Substitute: “39, ALEXANDER, SJ. Axial shortening of concrete columns and walls, Concrete, Vol. 35, No. 3, March 2001, pp. 36–38.” Page 75, Further reading Delete: “ALEXANDER, SJ. Axial shortening of concrete columns and walls, Concrete, Vol. 35, No. 3, March 2001, pp. 36–38.”

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Acknowledgements The Concrete Society would like t o thank the members of the working party for their efforts in preparing this report. The text in this report originates from guidance notes published internally by WSP, extended and amended to represent a consensus of the main authors’ three firms (WSP, Arup and Buro Happold). Valuable help has also been provided by John Forth of Leeds University, who contributed Chapter 7.

Published by The Concrete Society

CCIP-033 Published April 2008 ISBN 978-1-904482-42-0 0The Concrete Society The Concrete Society Riverside House, 4 Meadows Business Park, Station Approach, Blackwater, Camberley, Surrey CUI7 9AB Tel: +44 (0)1276 607140 Fax: +44 (0)1276607141 w.concrete,org.uk

CClP publicationsare produced by The Concrete Society (w.concrete.org.uk) on behalf of the Cement and Concrete Industry Publications Forum - an industry initiative to publish technical guidance in support of concrete design and construction.

CClP publicationsare available from the Concrete Bookshop at ww.concretebookshop.com Tel: -1-44 (0)7004 607777 All advice or information fromThe Concrete Society is intended for those who will evaluate the significance and limitations of its contents and take responsibility for its use and application. No liability (including that for negligence) for any loss resulting from such advice or information is accepted by The Concrete Society or its subcontractors, suppliers or advisors. Readers should note that publications are subject t o revision from time t o time and should therefore ensure that they are in possessionof the latest version. Printed by Alden Press, Witney. UK

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Movement, restraint and cracking in concrete structures Contents Members of the Proiect Working Partv

V

List of figures

V

List of tables

vi

Foreword

vi i

Notation

IX

1.

2.

Introduction

1

1.1

Overview

1

1.2

Types of movement

2

1.3

Sources of movement

2

1.4

Restraint to movement

2

1.5

Strain-induced forces

3

1.6

Cumulative effect

3

1.7

Why do cracks matter?

3

1.8

Avoiding cracking or controlling cracking?

4

1.9

Units of strain

5

1.10 Structure of the reDort

5

Magnitudes of free movements

6

21

Earlv-age contractions

6

2.1.1 Early thermal contraction

6

21.2 Autogenous shrinkage

7

2.1.3 Restraint and cracking due to early-age contractions

8

2.2

Effects of post-tensioning

9

2.3

Shrinkage

9

2.4

Choice of relative humidity

12

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2.5

2.6

3.

4.

5.

12

2.51 General

12

2.5.2 Coefficient of thermal expansion

13

2.5.3 Tensile strength

13

2.5.4 Seasonal temperatures

13

2.5.5 Daily temperatures

14

2.5.6 Solar radiation

15

2.5.7 Temperature range

16

Linear contraction and expansion

17

Understanding creep

18

31

Estimation of creep

18

3.2

Effective elastic modulus

20

3.3

Relief of stress by creep

21

Avoiding cracking or controlling cracking?

22

41

Avoiding cracking

22

4.2

Cumulative contractions

22

4.3

Minimum reinforcement in direct tension

23

4.31 Restrained structures

23

4.3.2 Controlling cracking

23

4.3.3 Immature concrete

24

4.3.4 Mature concrete

26

4.3.5 Flow chart

27

Internal restraint

29

51

Restraint by reinforcement - symmetrical sections

29

511 Restrained shortening

29

51.2 Tensile stress

30

51.3 Horizontal cracks in columns and walls

30

Restraint by reinforcement - asymmetrical sections

31

5.21 Curvature and deflection

31

5.2.2 Tensile stress

32

Temperature differentials

32

5.2

5.3 6.

Temperature movement

Surface restraint

34

61

In-situ toppings

34

611 Method of analvsis

34

61.2 Curvature and deflection

35

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6.2

7.

8.

Composite slabs on steel decking

36

6.21 Method of analvsis

36

6.2.2 Curvature and deflection

38

6.2.3 Codes and standards

38

6.2.4 Conclusions - deflection

38

6.2.5 Conclusions - cracking in the slab Edge restraint

39 40

71

Control of cracking

40

7.2

Restrained strain

45

7.3

Sjmmary

45

L

End restraint

46

81

Minimum reinforcement

46

8.2

Superstructure slabs

46

8.21 Spacing of movement joints

46

8.2.2 Design methods

47

8.2.3 Frame action

52

8.2.4 Post-tensioning

52

Basement ground slabs

53

8.3

9.

Calculation of crack widths

54

91

Principles

54

9.2

Minimum reinforcement content

54

9.3

Crack spacing

55

9.4

Edge restraint

56

9.5

End restraint

56

10. Mitigation measures

58

101 Planning requirements

58

10.2 Post-tensioned slabs

58

10.3 Reinforced slabs

59

10.4 Slab thickness

59

10.5 Aggregate selection

59

10.6 Cements

59

10.7 Control of pour sizes

60

10.8 Pour sequence

60

10.9 Pour strips

61

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1010 Column erids

62

10.11 Structural stability

62

10.12 Modified concrete mixes

62

10.13 Curing

63

10.14 Cooling the concrete

63

11. Practical applications 11.1

Basements

65

11.11 Introduction

65

11.1.2 Types of movement

65

11.1.3 Degree of restraint

65

11.1.4 Thermal and shrinkage movements

66

11.2 Case studv - basement floor slab

66

11.3 General observations

68

11.3.1 Incorporate proprietary waterproofing admixtures?

68

11.3.2Why not use tanking?

68

11.3.3The amount of reinforcement is too exDensive?

68

11.4 Multi-storey car parks

69

11.5 Movement a t movement joints in finishes

70

11.6 Axial shortening of columns and walls

71

References and further reading

iv

65

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Members of the Project Work ng Party Full members Stuart Alexander* John Clarke Tony Jones* John Morrison*

WSP Group Concrete Society (secretary) Arup Buro Happold

Corresponding members John Forth** Robert Vollum

* **

University of Leeds Imperial College

Main Authors Author for Chapter 7

List of fieures Figure 1

Example of the effect of early-age contractions on a car park structure.

Figure 2 Figure 3

Aesthetically acceptable crack widths. Flow chart illustrating the consideration of movements in the design process.

Figure 4 Figure 5 Figure 6

Autogenous shrinkage with time. Graphical representation of factors. Graph showing multiplication factors (‘ratios‘) for minimum and maximum temperatures for various return periods (R). Relationship between predicted temperature difference due to solar gain and slab thickness for different surfacing types for a specific location in the UK.

Figure 7

Figure 8 Graphs of effects of factors on the development of creep. Figure 9 Reduction over time of restrained tensile stress due to creep. Figure 10 Tensile strength and stress over time. Figure 11 Control of cracking by reinforcement. Figure 12 Comparison of surface zones in BS 8007 and BS EN 1992-1-1. Figure 13 Flow chart showing possible outcomes in restrained sections subject to linear tensile stress. Figure 14 Representationof shrinkage restrained by symmetrical reinforcement. Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20

Wall in Piccadilly Gardens, Manchester. Representationof shrinkage restrained by asymmetrical reinforcement. Contraction of in-situ concrete. Contraction of in-situ concrete slab on steel beam. Notation used in Steel Designers’Manual. End and edge restraint.

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Figure 21 Approximate regions o f domination of end (zone 1) and edge (zone 2) restraint in an infill wall. Figure 22 Conditions in a base-restrained wall after initial cracking. Figure 23 Cracking adjacent t o a primary crack (from Rawi and Kheder). Figure 24 Analytical model of wall o n rigid base. Figure 25 Primary cracks calculated at the free end. Figure 26 Effect of reinforcement content o n maximum crack width. Figure 27 Approach for determining restraint factor. Figure 28 Stresses induced in slab by 10°C temperature drop: Figure 29 Illustration o f frame deformation due t o slab contraction. Figure 3 0 Percentage shrinkage related t o time for a C32/40 concrete slab 3 0 0 m m thick at 50% RH. Figure 31 Percentage creep related t o time for a C32/40 concrete slab 3 0 0 m m thick at 50% RH. Figure 32 Deformed shape and cracking o f suspended basement slab. Figure 33 General view o f a typical basement car park. Figure 3 4 Close-up of cracks in Figure 33. Figure 35 Section through floor construction of car park basement in Figure 33.

List of tables Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9

vi

Typical early-age temperature rises. Relationship between Classes in BS EN 1992-1-1 and BS EN 197. Mean January and July temperatures for selected inland sites. Mean January and July temperatures for selected coastal sites. Design temperature range calculation for Stoke-on-Trent (example only). Characteristic values of tangent modulus. Minimum reinforcement contents in direct tension for immature concrete related t o strength class (total in both faces). Minimum reinforcement contents in direct tension for mature concrete related t o strength class (total in both faces). Values of modular ratio a, for concretes in indoor and outdoor environments.

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koreword The greater parts of codes of practice and textbooks on reinforced concrete focus on design to resist externally applied loads, deriving the reinforcement needed to resist axial loads, bending moments and shear forces. However, many concrete elements are lightly loaded or are affected principally by other actions, such as early-age contractions, temperature and humidity effects, creep, and long-term drying shrinkage. These all generate movements, and although they rarely determine the ultimate capacity they often affect serviceability, particularly cracking. The first step in understanding movement is to distinguish clearly between types ofmovement and sources of movement. Types (or categories or forms) of movement include deflection, shortening, sway, settlement, heave, and linear expansion and contraction. Sources of movement include dead and imposed loads, early-age contractions, long-term drying shrinkage, temperature variations, solar radiation, and post-tensioning.These all take place over different timescales, and time is an important parameter in understanding movement. It is also important to recognise that the sources act cumulatively, so that any cracking or deformation is usually at least the result of shrinkage and temperature added to early-age effects, and often with contributions from other sources. The importance of movement is highly dependent on whether or not it is restrained. Restraint occurs in many ways: internally, from reinforcement or temperature differentials; at an interface, when fresh concrete is placed on an older substrate or acts compositely with a steel beam; a t an edge, when a wall is poured onto a footing or a slab is poured against a previous pour; and between ends formed by stiff points, such as a slab between two cores or a basement floor between footings or pile caps. In practice, all restraint is partial, as apparently unrestrained elements are usually connected to structure with some stiffness, and very stiff restraints will usually ‘give’ under the huge forces that can be generated. There are two actions that alleviate the problems caused by restrained movement. The first is creep. While creep has some bad effects - increasingdeflection and shortening, for example - it is beneficial in reducingthe stresses induced by restraint, especially a t early ages when a 50% reduction can be achieved in a few weeks. The second is recognisingthat while the forces are potentially very large they are strain-induced, so that if the restraint is removed they reduce or even disappear. A final point is to understandcracking. Cracks occur in concrete when enough tensile stress

builds up to exceed the tensile strength, although some authors prefer to express this as when enough tensile strain builds up to exceed the critical tensile strain. The likelihood of this occurring is very difficult to predict, and the preferred strategy is to assume that cracks will occur and to provide enough reinforcement to control them. However, there will be situations when it is important to avoid cracking, and these need to be identified early and the right precautions taken throughout the life of the structure.

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The rest of this report explains all these points in more detail. It shows how t o make realistic estimates of the movements, the restraints and the resulting forces, and offers guidance on accommodating them in the design. It applies principally t o building structures, but special mention needs t o be made of the severe conditions encountered by open parking structures: they are exposed t o the full range of temperature and humidity throughout the year, and the top deck usually experiences solar radiation as well. However, although building structures are ultimately enclosed and maintained at fairly constant temperature and humidity, throughout the construction period they endure the same range of climate as car parks. Structural engineers are used t o estimating loads and resistances so as t o be on the safe side, but the philosophy here is to make the best estimate; thus probable (usually average) rather than minimum properties are used throughout. However, although the designer can exercise some control through the construction specification, allowances will still need t o be made for unknowns such as the vagaries of the weather and whether construction takes place in winter or summer. At the time of writing (2007), Eurocodes were being introduced but had not been generally adopted by practitioners. However, it was decided t o base the guidance on Eurocodes (mainly BS EN 1992-1-1(’))as they will supersede British codes during the life of this report. Differences from British codes are not significant, particularly in the context of movements where great accuracy is not expected to be achieved. This report is not claimed t o be the definitive work on what is a very difficult subject with a very limited research base. The text originates from guidance notes published internally by WSP, extended and amended t o represent a consensus of the authors’ three firms (WSP, Arup and Buro Happold). Valuable help has also been provided by John Forth of Leeds University, who contributed Chapter 7,

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Notation cover t o longitudinal reinforcement effective depth t o bottom reinforcement specified characteristic cylinder strength mean compressive strength (MPa) 10MPa (factor t o correct units and divide by 10)

h0

k kc

t0

X

mean value of tensile strength of concrete effective a t the time when cracks first occur notional size of cross-section (mm) coefficient which allows for the effect of non-uniform selfequilibrating stresses coefficient which takes account of the stress distribution within the section immediately prior t o cracking and of the change of the lever arm coefficient for effect of notional size factor dependent on the duration of the load coefficient which takes account of the bond properties of the bonded reinforcement coefficient which takes account of the distribution of strain maximum crack spacing age of concrete a t time considered (days) age of concrete (days) at beginning of drying shrinkage (usually end of curing) age of concrete at loading (days) depth t o neutral axis area of concrete effective area of concrete in tension surrounding the reinforcement area of concrete within the tensile zone minimum area of reinforcing steel within the tensile zone total area of reinforcement tangent modulus of elasticity of concrete modulus of elasticity at time t effective modulus of elasticity of the concrete modulus of elasticity of steel, usually taken as 200CPa second moment of area of the concrete section second moment of area of the gross cross-section restraint factor ambient relative humidity (%) (RH, = 100%) net first moment of area of the reinforcement about the neutral axis of the concrete section

ix

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coefficient of thermal expansion of concrete factor 3 for cement Class S , 4 for cement Class N, 6 for cement Class R factor 013 for cement Class 5,012 for cement Class N, 011 for cement Class R modular ratio between the €-values for steel and concrete coefficient for development of shrinkage with time factor for concrete strength coefficient dependent on relative humidity and concrete strength coefficient for humidity of environment = 1.55 [I - (RH/RHo)3] factor to allow for effect of concrete age at loading mean strain in concrete between cracks unrestrained (free) shrinkage total free strain due to shrinkage and thermal effects mean strain in reinforcement under relevant combination of loads ratio of reinforcement area to concrete section, AJAc minimum reinforcement ratio for immature concrete minimum reinforcement ratio for mature concrete A,lAC,,tt stress in the tension reinforcement assuming a cracked section or maximum stress in the reinforcement immediately before the formation of the first crack bar size creep coefficient

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1. Introd uction Concrete structures are affected by a number of physical processes that change their overall dimensions. This report discusses the nature, timescale and magnitude of these movements in buildings and similar structures.

1.I O V e W k W

The extent of the movements and the ways that they affect a structure depend on the materials, environment and construction methods used. It is therefore important t o estimate movements at the design stage and, where possible, restrict them t o acceptable levels. However, there are limits t o the extent t o which movements can be controlled, and one of the objects of design is t o accommodate movements in the most successful way. This report aims t o consider both the structural design and the construction sequence, with a view t o improving the performance of concrete structures. The consequence of restrained movements is often cracking which is the concrete’s way of accommodating the movement. In accommodating the movement, cracks can either be few and large or many and small. The latter is normally, but not always, preferred. A simple illustration of the effects of movement is given by the car park structure shown

in Figure 1. Here storey heights are small and column spacing large, resulting in short stocky columns and long-spanning beams. When the beam is cast it will contract due t o early-age effects. If the beam is cast all at once the large forces generated will be restrained by the columns. Assuming the columns are deemed to be infinitely stiff they will not deflect elastically but will rotate about point R, which will produce cracks a t the base of the columns as shown.

q

Figure 1 Example of the effect of early-age contractions on a car park structure.

C o n t ractio-

R

q

VlY

R

I

t-

Long span

4

To avoid this, the beam could be cast leaving out a short section (a pour strip) initially, thus eliminating any restraint t o longitudinal movement. The gap can then be concreted after the initial shortening has occurred in the rest of the beam.

In practice such an approach has knock-on effects on the construction process and does not relieve long-term movements. As the reinforcement cannot be continuous, the gap needs t o be long enough t o accommodate a lap. Nonetheless this remains a valid option; the alternative is t o design for the effects of the restrained movements.

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1.2 Types O f movement

A number of types of movement that may affect the structure can be identified, as follows: 0

Deflection. Vertical movement within the span of a beam or slab. Settlement, heave. Downward or upward movement of a foundation or of a whole

building or structure. 0 Axial shortening. Vertical downward movement of columns or walls. 0 Linear expansion, linear contraction. Horizontal lengthening or shortening of members such as beams and slabs. The behaviour of concrete is very different between expansion (which causes compression) and contraction (which causes tension). 0 Sway (or drift). Horizontal movement within a storey height or of the whole building or structure.

1.3 Sources O f movement

A number of sources of movement can be identified, as follows: 0

0

Earlyage 0 Early thermal contraction and autogenous shrinkage. Longterm 0 Drying shrinkage (often called just 'shrinkage').

0

0 Creep. Seasonal 0 Seasonal temperature variations. Shortterm

0 Daily/weekly temperature variations. 0 Solar radiation. Load induced 0 Post-tensioning, which causes both immediate and long-term contractions. 0 Dead and imposed loads: in the context of this report these are generally only

relevant to axial shortening, except when applied to non-vertical members, e.g. raking columns or transfer walls. Again these cause both immediate and longterm contractions. 0 Soil pressures:these are generally not relevant, although they can counter contractions in basement slabs. 0 Seismic loads: these are not considered in this report.

1.4 Restraint t o movement

There are four basic types of restraint to movement: 1. Internal restraint may be provided by the reinforcement. This can resist shortening of the concrete and occasionally leads to cracking. If the reinforcement is asymmetrical it will lead to deflection. Temperature variations will not normally have a significant effect as steel and concrete have similar coefficients of thermal expansion. Differential movement may also occur when one part of the concrete section wants to expand or contract more than another. Examples arise where temperature differentials exist, or where differential drying shrinkage occurs, typically in thick sections.

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2. Surface restraint. Typically this occurs when an in-situ topping is cast onto an older substrate. It also occurs in composite floors because the contraction of the concrete slab is resisted by the supporting steel beams. Surface restraint leads t o deflection and cracking, especially in composite slabs. 3. Edge restraint occurs when a wall is cast onto an older and bulkier footing or when a slab or wall panel is cast against one poured previously. 4. End restraint occurs typically in a structure linking two or more separated cores or shear walls, but also in basement floors restrained by piles or pile caps or even by friction with the soil.

1.5 Strain-induced forces

Two points are important when considering the effect of movement on structures. The first is that if the movements are restrained the magnitude of the resulting forces can be enormous. So, for instance, the movements in the floors connecting two cores of a building will generate forces which will either pull together or push apart the cores or result in deflections or cracking in the floor. The abutments of an integral bridge will similarly be affected by movements in the deck. The second point is that although the forces can potentially be very large, they are strain induced. This means that if the restraint is reduced, e.g. by cores deflecting or the concrete cracking, the forces reduce or even disappear.

1.6 CUmUkiVe effect

It is common practice t o talk about cracks in concrete by referring t o their source, such as

‘early thermal cracks’ or ‘shrinkage cracks’.This ignores two important aspects. First, what causes a crack is not temperature or shrinkage but simply that the tensile stress has exceeded the tensile strength. Second, the stress in a restrained member such as a basement wall or floor builds up over time from the cumulative effect of the contractions described above, albeit relieved somewhat by creep.

1.7 Why do cracks matter?

The short answer is ‘because people don’t like them’. Campbell-Allen(2)investigated the relationship between crack width and the distance from the viewer for nine categories of structure ranging from ‘little used buildings’ t o ‘monumental buildings’. His conclusions are given in Figure 8 of Concrete Society Technical Report 22, Non-structural cracks in concrete(3),which is reproduced here as Figure 2. So-called ‘hairline’ cracks are generally no more than 015mm wide but are usually visible from up t o about 2m away. Visibility is exaggerated if the cracks collect dirt or exude accretions. Where the concrete can get wet, cracks become highly visible when the general surface has dried but the cracks are still wet. The generally accepted limit of 0.3mm is visible from 5m or more, and so represents the structural engineering community’s idea of acceptability rather more than that of a lay person.

3

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, 1

Figure 2 Aesthetically acceptable crack widths.

9

BS 8110 limit

E

7

-

E6 W

c

2 5 O M

g 4 >

3 1

2 1

0

I

0.1

0:2

0:4 Crack width (mm)

0:3

0:s

0:6

0:7

What about corrosion? It appears intuitive that cracks permit water and oxygen t o reach the reinforcement and therefore promote corrosion. However, it is generally understood that there is no direct relationship between long-term durability and surface crack width; see for example Concrete Society Technical Report 44(4).So we have t o conclude that the objection is principally aesthetic.

1.8 Avoiding cracking or controlling cracking?

It is important to realise that reinforced concrete will generally crack. It is only when cracks form that the reinforcement starts t o carry any appreciable load; prior t o that the concrete is effectively behaving as unreinforced. When considering the effects of movement on a structure, there are two approaches that can be adopted. The first is t o avoid cracking, by limiting the stresses induced in the concrete by restricting the amount of movement and/ or the level of restraint. The second is t o assume that cracking will occur and t o control crack widths by providing sufficient correctly detailed reinforcement. The former approach will generally not be practicable and hence the design philosophy is t o ensure that there is sufficient reinforcement in critical regions of the structure.

Avoiding cracking is difficult and risky; even with great care, any number of unforeseen events can conspire t o cause sufficient contraction or sufficient restraint (or both) for the tensile stress t o exceed the tensile strength so that the concrete will crack. Designing t o control cracking is more reliable; if the reinforcement is stronger than the force which causes the crack, any cracks will be controlled so that they will usually not be unsightly or leak excessively.Also, the more reinforcement that is provided, the finer the cracks will be. This report is generally based on the premise that concrete will crack but that cracking should be controlled. However, some guidance on avoiding cracking is given where relevant.

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1.9 Units Of Strain

1.10 Structure O f the report

It is convenient t o measure strains in units of strain x 10-6.Theseunits are called 'microstrain' ~ or Olmm/m. and abbreviated t o the symbol F E . In numerical terms, 1 0 0 is~100mm/km

The structure of the report is illustrated in Figure 3, which shows the various aspects that need t o be considered in the design process.

Figure 3 FLOW chart illustrating the consideration of movements in the design process.

1

START

Deflection Settlement/heave Axial shortening Linear expansion Linear contraction Sway (or drift)

occur in m y structure?

Technical Report 5 8 N o t included Section 11.6 Section 2.6 Section 2.6 N o t included

i

Estimate free movement (contraction, expansion) at each key stage - early-age, long-term

I

Contribution t o shortenine

Alleviation of restraint

I

Seasonal temperatures Short-term temperatures (including solar radiation) Shrinkage Post-teisioning effects

Section 2.5.4 Section 2.5.5 Section 2.3 section 2.2

free movement

movements

Understanding creep

Chapter 3

Internal restraint Shortening Horizontal crackine

Chapter 5

I Surface restraint Contraction of toppings Slabs in composite construction

+

Edge restraint Successive pours Walls on footings

End restraint Superstructures between stiff supports Basement floor slabs

//.h.

7 )

Accept kovements

Chapter 6

Chapter 7

Chapter 8

I Pour seauence Modified concrete mixes

1

5

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rM,agnitiilidenof free movements

2. Magnitudes of free movements In the design of concrete members, the following have to be considered in detail: early-age contractions long-term shrinkage movement due to temperature variations

2.1 Early-age contractions 2.11 Early thermal Contraction

The reaction of Portland cement with water is an exothermic process, i.e. one in which excess heat is generated.The potential rise in temperature may be as high as 13°C per 100kg/m3of cement when using CEM I cement alone in thick sections; for typical structural concretes (28/35 to 40/50MPa) the cement content may be 330-400kg/m3 and the potential rise thus over 50°C. However, in practice the actual temperature rise is much less because heat is lost through the surfaces, and is dependent on such factors as the dimensions of the pour, the insulation provided by the formwork, and the placing and ambient temperatures. While the temperature is rising the concrete behaves in a relatively plastic manner so that the only result is a small increase in volume. When the concrete starts to cool to ambient temperature it has sufficient stiffness to develop tensile stress if externally restrained, and may even crack. The amount of contraction is calculated by multiplying the temperature drop by the coefficient of thermal expansion of concrete. Methods of estimating the temperature drop are given in a number of sources, e.g. ClRlA 660, Early-age thermal crack control in concrete(5), and Coodchild(6);the latter shows that for slabs only 300mm thick the temperature drop can be as much as 25"C, typically producing a free (unrestrained) early-age contraction of 3 0 0 p ~ . Replacing some of the Portland cement by ground granulated blastfurnaceslag (ggbs) or fly ash (pfa or pulverised-fuelash) is an effective way of reducing the rate of heat generation (see Table 1).The values have been derived from ClRlA 660(5)and are based on a 300mm slab cast in the summer with a placing temperature of 20°C on 19mm plywood formwork for a concrete specified as C32/40.

Table 1 Typical early-age temperature rises.

6

CEM I32,5N

340

31

50% ggbs

355

21

75% ggbs

410

18

30% fly ash

365

20

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Embedded reinforcement follows the same temperature profile, and as the coefficient of thermal expansion of steel is very similar to that of concrete there are usually no adverse effects. However, in deep pours (over about 0.75m), differentials in temperature cause internal restraints that can lead to cracking. This topic is examined in more detail in ClRlA 660(5)and is not covered further in this report.

21.2Autogenous shrinkage

Autogenous shrinkage is an important phenomenon in concrete with a low waterkement (w/c) ratio. In this context, cement means total cementitious material, i.e. including any ggbs, fly ash or silica fume. Unless the concrete is cured early and thoroughly with water, significant autogenous shrinkage (sometimes called chemical shrinkage or self-desiccation) can occur during the first few days after casting. This can lead to cracking which may negate the intended benefits of using high-performance concrete. It can also be important when in-situ concrete is placed over older concrete as in various forms of hybrid construction; see Chapter 6, Surface restraint.

Mechanism of autogenous shrinkage The process of water combining chemically with cement is called hydration. At lower w/c ratios all the water is rapidly drawn into the hydration process and demand for more water creates very fine capillaries.The surface tension within the capillaries causes autogenous shrinkage. In thin sections, if the surface of the concrete is kept continuously wet, water is drawn into the capillaries and the shrinkage does not occur. Indeed, a small amount of swelling has been observed in tests on small specimens. Shrinkage-reducingadmixtures lessen the surface tension thus reducing the shrinkage, but should still be used with thorough water curing. However, curing may not be effective in eliminating autogenous shrinkage in practice. In thick pours with low w/c ratio the zone of curing is limited to the surface few centimetres of depth and autogenous shrinkage may still be significant within the bulk of the section. Another suggestion is to use lightweight aggregates thoroughly pre-soaked with water. This supports the process called ‘internal curing’ and may overcome the issue of limited curing zones in thick sections. However,this has not yet been fully researched. Note that autogenous shrinkage is separate from and additional to conventional drying shrinkage, which will start when water curing ceases and may be estimated by the methods described in Section 2.3.

Numerical evaluation The only code of practice to cover autogenous shrinkage is BS EN 1992-1-1(’).This includes a formula: = 2.5

(tk- 10)

(PE)

(BS EN 1991-1-1 Expression 3.12)

where: specified characteristic cylinder strength

fck

7

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Figure 4 Autogenous shrinkage with time.

Autogenous shrinkage with time 120 100

80

8 60 40

20 0 1

10

100 1000 Time (days)

10000

100000

The progression with time is also given and is shown in Figure 4 It can be seen that much of the autogenous shrinkage occurs very early in the life of the

concrete and is all but complete within 100 days. This is very different from conventional drying shrinkage. The assumption in BS EN 1992-1-1that autogenous shrinkage is directly related to specified strength with no consideration of mix proportions is clearly an approximation. However, as discussed above, early curing is also critical to the total autogenous shrinkage that occurs. The values in BS EN 1992-1-1 are quite low (e.g. 5 5 for~strength ~ class 32/40) compared to those given by Altoubat and Lar~ge(~), which suggests that water curing is assumed.

Curing The requirements for water curing are quite onerous.The surface of the concrete must be prevented from drying from the moment at which the concrete has been finished. As soon as possible thereafter water must be applied to the surface and this must then be kept continuously wet for several days. Side forms of deep members should be released so

that water can be fed to these surfaces also. The preferred method of applying water is by mist spray; reports mention equipment used for bowling greens or plant nurseries. Failing this, hessian can be used but should be continuously watered with hoses and covered with polythene. This will not be practicable for most projects and so it is essential that the effects of autogenous shrinkage are considered.

2.1.3 Restraint and cracking due to early-age contractions

8

Early-age contractions all occur in the first seven days or so. If the contractions are restrained, tensile stress builds UP and can lead to cracking.There are many potential sources of restraint; the most common is adjacent elements poured earlier, especially walls cast on substantial footings but also slabs cast against previous pours. Others include toppings cast on older substrates, slabs in composite construction (see Chapter 6) and ground slabs connected to footings or piles.

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The risk of cracking is difficult t o predict with any great precision. If in doubt, the simplest and safest policy is t o assume that cracking will occur and provide reinforcement to control it. This is discussed in Section 4, leading to recommendations of reinforcement contents higher than previously recommended (but comparable t o BS EN 1992-1-1).

2.2 Effects Of posttensioning

Post-tensioned slabs behave differently t o non-stressed reinforced concrete slabs in two key ways: 1. The axial compression will cause a shortening of the slab in addition t o any shrinkage or temperature effects. Initial elastic shortening can be controlled by the use of pour strips (see Section 10.9) but it should be acknowledged that creep continues for a significant period and there is likely to be further shortening after the concreting of any pour strips. In particular, as for shrinkage, creep increases as the humidity of the environment reduces, so may increase significantly once the slab is enclosed. 2. Because the concrete is in compression it is far less likely t o crack due t o any restraint forces. This means that the axial stiffness of the slab will be greater than that of a reinforced concrete slab due t o the lack of cracking. Therefore the forces that can be exerted on any restraining structure will be that much greater.

These points apply to an extent to all slabs with an axial compression in them, thus including slabs spanning between perimeter walls in basements. Where axial compression is present in a slab, the consequences on the surrounding structure are likely t o be greater than for a normal reinforced concrete. Nonetheless the effects can be calculated and accounted for in the design; indeed the lack of cracking makes analysis easier. The axial compression in the slab will either prevent or significantly delay cracking in the slab, which may be beneficial from a visual or waterproofing point of view.

2.3 Shrinkage

Strictly, shrinkage should be called long-term drying shrinkage but the one-word abbreviation is common practice, although BS EN 1992-1-1 uses drying shrinkage t o distinguish it from autogenous shrinkage, which is discussed in Section 2.1.2. Drying shrinkage strain is a function of the migration of water through the hardened concrete and therefore develops slowly. When concrete is placed it usually contains more water than required for full hydration. Concrete which is buried may remain saturated but usually concrete is exposed to drying conditions. Both the aggregate and the cement matrix shrink as water is lost, resulting in overall shrinkage of the concrete. The rate of shrinkage depends on the humidity of exposure and the section size, and decreases with age. The use of good-quality aggregates and low w/c ratios will reduce the shrinkage. Although retention of moisture by curing until the concrete is more mature is good practice for other reasons, it has little effect on the final amount, but does delay the onset of drying shrinkage.

9

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Magnitudes of free movements

BS EN 1992-1-1clause 3.1.4 gives a method for determining the strain.Thedrying shrinkage strain (for unreinforced concrete) is calculated as a basic value dependent on relative humidity and concrete composition modified by a factor for variation with time and a factor for notional size, that is:

This can be rewritten to include the expression for the basic drying shrinkage, as follows:

where: P,,(t, t,) coefficient for development of shrinkage with time (also size dependent), see

BS EN 1992-1-1clause 3.1.4,taken as 1.0 where t = 00 (when shrinkage is

complete) = ( t - t, ) / [ ( t t,)

k,

ads, adsZ

fc, fcmo

P,,

+ 0.04dh,3]

where: t age of concrete a t time considered (days) age of concrete (days) a t beginning of drying shrinkage (usually end of t, curing) h, notional size (mm) of cross-section = 2A)u where U = perimeter coefficient for effect of notional size, ho,see Table 3.3 of BS EN 1992-1-1 factor 3 for cement Class 8, 4 for Class N, 6 for Class R factor 0.13 for cement Class 5, 0.12 for Class N, 0.11 for Class R mean compressive strength (MPa) 10MPa (factor to correct units and divide by 10) coefficient for humidity of environment = 1.55 [I- (RH/RH,)3] where: RH ambient relative humidity (%) RH, 100%.

Similar to creep, shrinkage is not dependent on concrete strength as such, but f , , is included in the calculation of shrinkage. This is to account for the w/c ratio since generally the lower the w/c ratio, the higher the concrete strength. Shrinkage decreases with decreasing w/c ratio and decreasing cement content. The type of cement and whether it is a slowly hardening cement (Class S), has ordinary early strength development (Class N) or is a rapidly hardening cement (Class R) is also taken into account in the calculation. It is important to note that these designations (R, N and 8) are not the same as those in

the cement standard, BS EN 197(*).The BS EN 1992-1-1 Classes are related to the cement designations as given in Table 2.

10

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Table 2 Relationship between Classes in BS EN 1992-1-1(') and BS EN 197(*).

-_

-

-r

CEM 42 5R, CEM 52 5N and CEM 52 5R ---

1--

-__

-

-

--

1' CEM___ 32 5N

iL-.

-

-

~

~

~

-1

1

~-

---I _

_

These designations are for factory-produced cements. There are no official general rules for cements blended in the mixer. However, Chapter 8 of How to design concrete structures using Eurocode Z(9)notes that:

"At the design stage it is often not clear which Class should be used. Generally Class R should be assumed. Where the ground granulated blastfurnaceslag (ggbs) content exceeds 35% of the cement combination or where fly ash (pfa) exceeds 20% of the cement combination, Class N may be assumed. Where ggbs exceeds 65% or where fly ash exceeds 35% Class 5 may be assumed."

I The graphs in Figure 5 illustrate the factors described above. An approximate value of the

Figure

drying shrinkage strain can be found by multiplying the relevant values from the graphs.

Graphical representation of factors.

Factor for concrete composition

Factor for notional size and age 1.2

F

0

1

m

!.

- 0.8 m

._

0.6

-

0.4

Y

E 0

b 0.2

Y

m

Y

0 30

40 50 60 Mean compressive strength,!,,

+ Cement Class R

-A-

70 (MPa)

1

80

Cement Class S

+ Cement Class N

10

100 Age t-ts (days)

1000

t h, = 100

6 h, = 300

+h, = 200

++ h, = 500

10,000

Factor for relative humidity 1.8 1.6 C

9 1.4 Y

g

1.2

8

1.0

' b +

0.8

b 0.6 Y 0.4

Y

LL

0.2 0.0

0

10

20

30

40 50 60 Relative humidity (%)

70

80

90

100

11

_

_

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I

Magnitude5 of free movements

Most structures spend the early part of their lives in an external environment before they are enclosed. As BS EN 1992-1-1 allows shrinkage to be calculated a t any time, it is possible to calculate the shrinkage up to enclosure based on an external humidity; final shrinkage can then be calculated based on the internal humidity. The principal effect will be to reduce the early shrinkage rather than reducingthe overall shrinkage. Although shrinkage is largely irreversible,clause 7.4 of BS 8110-2(’0)notes:

“Concrete exposed to the outdoor climate in the UK will exhibit seasonal cyclic strains of 0.4 times the 30 year shrinkage superimposed on the average shrinkage strain; the maximum shrinkage will occur a t the end of each summer.”

No similar guidance exists in BS EN 1992-1-1,presumably due to the variations in climate across Europe. It would therefore seem appropriate to adopt similar values. Due to the fact that the maximum shrinkage occurs a t the end of summer, it is unlikely to coincide with the lowest temperature (or minimum shrinkage with maximum temperature), and as the seasonal temperature effects are usually greater, the seasonal variation of shrinkage can generally be ignored. As mentioned previously, the above method is applicable to unreinforced concrete. BS EN 1992-1-1 does not address the need to adapt this for reinforced concrete. However,

Section 4.1 of BS 8110-2 gives a reinforcement modification which is usually sufficiently accurate to use with BS EN 1992-1-1 shrinkage predictions. It can be derived from first principleswith appropriate assumptions on creep, see Section 5.1.1.

2.4 Choice O f relative humidity

Both creep and shrinkage are sensitive to the ambient humidity of the environment, so it is important to adopt realistic values.The indoor environment of offices is usually taken as 45%, although a higher figure, say SO%, could perhaps be taken where natural ventilation is provided; 55% may be appropriate for dwellings. The 12-month average outdoor humidity in Britain ranges from 75% in the drier South-East and East Anglia to over 90% in the wetter North-West and the western side of Scotland. However, humidity should not normally be taken higher than 85%. The seasonal variation is significant, perhaps +IS%, but only needs to be taken into account in very sensitive structures constructed in spring or early summer. BS 8110-2 recommends an outdoor humidity of 85% for the UK which is reasonable for most locations, given the other unknowns; however, more accurate historic data can normally be obtained from various sources.

2.5 Temperature movement

2.5.1Celleral

12

Daily and seasonal temperature variations cause dimensional changes to outdoor structures and to a lesser extent to indoor structures Solar radiation can raise the temperature significantly above the shade temperature In reinforced concrete elements, temperature affects concrete and steel alike, their coefficients of thermal expansion being similar

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Because of the thermal mass of heavy structures such as bridges, diurnal temperature changes (exacerbated by solar radiation) produce thermal gradients within the deck which cause deflections as well as stresses if the movement is restrained. This aspect is not considered further in this report, except in the case of car parks as discussed in Section 11.4.

2.5.2 Coefficient Of thermal expansion

Movements resulting from temperature effects are usually reversible. The coefficient of thermal expansion of concrete can vary significantly. BS EN 1992-1-1 suggests that if no more accurate information is available a value of I O ~ E / " C(10 x 10-6/oC) should be used. However it has been common practice within the UK t o use a value of 12pd"C which is consistent with BS 8110-2 for gravel aggregate. BS 8110-2 also gives values of 10pd"C for granite aggregates and 8.Opd"C for limestone aggregates. It therefore appears that the BS EN 1992-1-1 value is a mean value independent of aggregate type. Generally, higher coefficients of thermal expansion are more onerous and, unless the actual aggregate type is known, i t is recommended that in the UK the value of 12pd"C be used. This report adopts this value throughout. The coefficient of thermal expansion for lightweight aggregates is normally lower but is subject t o even greater variability. Further advice o n the appropriate choice of coefficient of thermal expansion is given in ClRlA 660(5).

2.5.3 Tensile strength

The tensile strength of concrete reduces from its short-term value if the tensile stress is sustained; a reduction factor of 0.7 can be applied for stress sustained for more than 30 days. This time period is much less than was previously thought, but has come out of research into the loss of tension stiffening with time, see Concrete Society Technical Report 59("). It is therefore important t o distinguish between daily and weekly fluctuations which can be considered as short-term, and seasonal effects which should be treated as long-term.

2.5.4 Seasonal temperatures

Tables 3 and 4 overleaf give the mean temperatures at sites in the UK forJanuary and July averaged over the 30 years from 1971 t o 2000. For most sites in the UK, the mean temperature difference between winter and summer is around 11-12°C. Note also that city centres are hotter than their surrounding areas.

13

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temperatures ("C) for London (Greenwich) selected inland sites.

52

18 2

Lowestoft

42

16 6

36

14 a

Torbay (Teignmouth)

64

171

40

15 7

Tenby

58

15 8

34

15 3

Southampton (Everton)

53

16 7

42

16 3

Kirkwall

39

12 7

Birmingham (Sutton Bonnington) 3 8

16 6

Aberdeen (Craibstone)

31

13 a

Bristol (Lyneharn)

39

16 6

Newquay (St Mawgan)

62

161

Bury S t Edmunds (Wattisham)

35

16 6

Holyhead (Valley)

58

15 7

Cardiff

50

172

Hull (Cleethorpes)

43

16 2

Londonderry (Carmoney)

55

15 7

Blackpool

43

16 0

Belfast (Aldergrove)

42

15 2

Eastbourne

43

16 0

Edinburgh

FarrightTabLe 4 Mean January and July Glasgow (Paisley) temperatures ("C) for selected coastal sites. uponTyne (Durham)

Manchester (Airport)

2.5.5 Daily temperatures

Maps showing I-in-50years minimum and maximum shade temperatures are given in BS 5400-2(12) and in the UK National Annex t o EN 1991-1-5(13). Note that corrections need to be applied for height above sea level by subtracting 0.5"C per 100m height for minimum temperatures and 1.O"C per 100m height for maximum temperatures. A graph showing correction factors for return periods other than 50 years is reproduced in Figure 6. A return period of ten years is probably sufficiently onerous for typical movement

assessments; this is achieved by multiplying the 50-year minimum temperature by 0.72 and the maximum by 0.9. A map minimum of -14°C would then reduce to -10°C. The 50-year return period values should be considered for open structures and top storeys if the consequences of movement could be damaging. Figure 6 Graph showing multiplication factors ('ratios') for minimum and maximum temperatures for various return periods (R).

200 150 100 70 50

e

20 /

10 -

I

5-

/

21 0.4 0.5 /#

0.6

0.7

0.8 0.9 Ratios

14

1.0

1.1

1.2

1.3

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These temperatures are minima occurring in the early hours of the morning and maxima during the afternoon, both lasting for a few hours a t most before easing off. Most structures have sufficient mass to heat up or cool down more slowly than this. This 'thermal inertia' means that the temperature to be used for movement calculations will be less extreme. An exact calculation of this effect is quite complex, and a realistic estimate is all that is

required. For a 250mm thick slab in a multi-storey car park, an alleviation of extreme temperatures by 2 - 3 O C seems reasonable.

2.5.6 Solar radiation

Surfaces open to the sun experience a further rise in temperature due to solar radiation. This produces two effects. The first is to expand the top surface relative to the underside, leading to upwards deflection a t mid-span, often accompanied by rotation a t the supports. The opposite effect in winter, of the exposed surface becoming colder than ambient, is only minor and can usually be ignored. The second is to increase the average temperature of the whole section, thus increasing the linear expansion above that from ambient (shade) temperature. These effects are particularly important in exposed structures, most notably multi-storey car parks (see also Section 11.4) and should always be considered.The surface treatment often includes a black top. The selection of surfacing is particularly important as shown in Figure 7. This shows the predicted maximum temperature difference between the top surface and soffit through slabs with different thicknesses and surfacing types modelled using finite-element software for a specific location in the south of the UK. The soffit temperature remains at ambient.

Figure 7 Relationship between predicted temperature difference due to solar gain and slab thickness for different surfacing types for a specific location in the UK.

-

1

25

t 50mm asphalt

E

t Bare concrete or light

W

5

grey membrane

20

+ Dark grey membrane

U

< ?!

15

W Q

$

c

U W c

10

._

U

?!

n

5 100

200 300 400 Slab thickness (mm)

500

15

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I

An estimation can also be made using BRE Digest 228(14)which gives minimum temperature -2OoC, maximum +45OC for light colour and +6OoC for dark. Assuming the maximum shade temperature is 35"C, the increases for solar radiation are 10°C and 25°C respectively. Judged from -20°C, these are 1 in 120 years figures, so correcting the increases t o 1 in 10 years reduces 10°C and 25°C t o 9°C and 22°C respectively. Bare concrete is quite light in colour, so assuming it is one-third up from 'light' would give an increase of 13OC. Dark finishes such as asphalt would have t o be treated as 'dark' but the thickness of the asphalt will affect the temperature of the top o f the concrete beneath and the insulation properties of the asphalt should also be taken into consideration. (Note that Appendix C in BS 5400-2 indicates that an asphalt thickness of over 7 0 m m is needed t o reduce the maximum surface temperature differential over the minimum concrete temperature from that experienced by bare concrete, but these results were based o n modelling the asphalt as having the same thermal properties as concrete and underestimate the benefit of the insulation properties.) The data in Figure 7 and BRE Digest 228 presumably allow for thermal inertia, so any allowance made previously should be added back in.

2.5.7 Temperature range

The final piece o f data needed t o calculate the likely temperature range is the casting temperature. This must be expressed as a 24-hour mean ambient temperature, as the rise above ambient and fall back t o it have been accounted for in early thermal contraction. For design, it will usually be necessary t o assume casting could take place at any time of the year and at any temperature, except that casting below 5°C is prohibited in most specifications (and precautions taken t o prevent the concrete falling below this temperature). However, extreme values are not required, as this would result in t w o extreme values being taken together. A winter temperature of +5"C is probably appropriate; for summer, a figure midway between the July mean and the daily maximum calculated as above could be taken. As an example, data calculated for Stoke-on-Trent could be assembled as in Table 5

Table 5 Design temperature range calculation for Stoke-on-Trent (example only).

Shade temperatures

-1 8

Allow for city centre (estimated)

-18

Correct to ten-year return

0.72 x (-15) =-11

Allow for thermal inertia (+3, -3.5)

-11

+ 3 = -8

No change

0.9 x (+34)= +30.5 +30.5 - 3.5 = +27

Seasonal means

+3

+16

Casting temperatures (24-hour mean)

(27 + 16)/2= +21.5

specification limit = +5

Range casting to seasonal

+3 - (+21.5)= -18.5 (drop)

+16 - (+5) = +11 (rise)

Range seasonal t o daily extreme

-8 - (+3)= -11 (drop)

+27 - (+16)= +11

Total range

-29.5 (drop)

+22 (rise)

nla

+13 i3.5 = +16.5

Solar radiation (concrete surface)

16

+34

+ 3 = -15

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2.6 Linear COntraCtiOn and expansion

At any point in time, the combination of the movements discussed above will lead to

linear contraction or expansion. In the early days, contraction will dominate. However, this is quite rapidly partially relieved by creep (see Chapter 3), so that if the ambient temperature rises - as is likely in the first summer of structures cast in winter - expansion can occur. In practice, this is usually unimportant, as the movement is unlikely to be very great and the resulting compression in the concrete will not produce any noticeable effects. As the seasons progress, particularly in structures cast in summer, drying shrinkage will set in, temperatures will drop, and the overall effect will be contraction. This is of more concern because if restraint is present, tension is induced and cracking can occur. This is discussed in more detail in Section 4.2.

17

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3. Understanding creep When concrete is subjected to long-term stress it gradually deforms with time; this process is called creep. The amount of creep depends on the ambient humidity, the dimensions of the element, the composition of the concrete, the maturity of the concrete when the load is first applied, and the magnitude and duration of the loading. The ratio of creep movement to initial elastic movement is known as the creep coefficient, q(t,to).

3.1 Estimation O f Creep

The final creep deformation of concrete, a t time t = 03 for a constant compressive stress applied a t age t = 0, is given by:

where:

q(w,to)creep coefficient as below f,

tangent modulus, which in accordance with BS EN 1992-1-1 may be taken as 1.05 times the secant modulus, Ecm.This is the value a t 28 days and should be used rather than f,,(t), the value a t age t days, see Section 3.2.

BS EN 1992-1-1 can be used to give an approximate value of the creep coefficient, where

the compressive stress is not greater than 0.4Sfc,(t0)at an age to,the age of the concrete a t the time of loading. The creep coefficient at any time after loading can be calculated from:

where: 'p0

notional creep coefficient = (PRH P(fJ

Pko)

In the above equations: P,(t, to) coefficient for development of creep with time after loading = [ ( t - to)/(&

+t- t0)p

where: t to

0,

age of concrete a t time considered (days) age of concrete a t loading (days) coefficient dependent on relative humidity and concrete strength = 1.5 [I + (0.012 RH)18] h, for fcmI 35 and 1.5 [I + (0.012 RH)18]h, + 250a, I 1500a, for fcm 2 35 where: RH

a,

h,

18

relative humidity (%) concrete strength coefficient = (35/fCm)O5 notional member size (mm) = 2A)u

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qRH factor t o allow for the effect of relative humidity [I + (1 - RH/100)/(01 x 'dh,)] for fcmI35 and {I+ [(I - RH/100) a,/(Ol x 3dh,)]}a2for fcmz 35 P(f,) factor for concrete strength = 16.8/dfcm where: fcm mean compressive strength (MPa) factor t o allow for effect of concrete age a t loading = V(O1 + t , O 2 )

P(t,)

The effect of the type of cement on the creep coefficient may be taken into account by modifying I, as follows:

where: a -1 for cement Class 8 0 for cement Class N a 1 for cement Class R a Be/ow/eft Figure 8a

Effect Of timeon thedevelopment Of creep (to= 90 days, R H = 50%, fc, = 40MPa, ho=250rnrn,c[ass N).

Figure 8b Effect of relative hurnidityonthe development of creep (to= 90 days, t = m, f,, = 40MPa, h, = 250mrn, Class N).

The graphs in Figures 8(a)-(e) illustrate the effect on the development of creep of varying the cement class, the relative humidity, the notional size, or the duration of drying. The creep coefficient can also be determined graphically using the figures in BS EN 1992-1-1. However, due t o the complexity of the relationships, this method is not easy t o use accurately. It is probably more straightforward therefore t o calculate creep directly using spreadsheets.

1.8 3.0

1.6

2.5

1.4 c

c

E

C

._ 1.2 U ._ 1.0

.$ 2.0 ._

5

r

8

0.8 a

E

U

1.5

CL

$

0.6

1.0

U

0.4

0.5

0.2 0.0 10

100

1000

10,000

Concrete age (days)

100,000

0.0 100

80

60

40

20

0

Relative humidity (%)

19

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1.76 1 -

3.0

1.76

2.5

..-E

Y

.-5

Y

2.0

1.75

U

= 1.5

1.75 1.74

n

aJ

;1.0

$ 1.74

0.5

1.73

U

1.73

S

0.0 0

Above left

10 20 30 40 SO Mean concrete strength (MPa)

60

2.5

c1

2.-aJ 1.5 8 e 1.0

Figure 8d

2

U

Figure 8e

0.5 0.0

Effect of notional size on the development of creep. (to= 90 days, t = -, RH SO%, fcm = 40MPa, Class N).

3.2 Effective elastic modulus

2.0

aJ c

Effect of cement class on the development of creep. (to= 90 days, t = m, RH = SO%, h, = 250mm, fcm= 40MPa). Rght

R

Figure 8c

Effect of concrete strength on the development of creep. (to= 90 days, t = -, RH = 50%. h, = 250mm. Class N). Aboveright

N Cement class

0

100

200 300 400 500 Notional size (rnrn)

600

It is often convenient t o carry out calculations using an effective elastic modulus. The

expression for stress-dependent strain can be written t o give the following: Stress-dependent strain = initial strain at loading + creep strain at time t after loading

Dividing by ocand rearranging gives:

where: EJt) modulus of elasticity at time t E, tangent modulus as above.

20

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However, it is often acceptable to assume that EJt) commonly used form:

= E,;

this simplification leads to the

Typical characteristic values of the tangent modulus of elasticity, Ec, are shown in Table 6. Table 6 Characteristic values of tangent modulus.

20

28

30

32

30

38

33

35

35

43

34

36

40

48

35

37

50

58

37

39

The relationships used to calculate the creep coefficient are empirical, calibrated on the basis of laboratory tests. Only those parameters which are normally known to the designer - characteristic compressive strength, dimensions of the member, mean relative humidity, age a t loading, duration of loading and type of cement -are taken into account. However, it should be noted that creep of concrete is not dependent on its compressive strength or age at loading as such, but rather on its composition and degree of hydration. Creep of concrete decreases with decreasing w/c ratio, decreasing cement content and increasing degree of hydration. BS EN 1992-1-1 also allows for modifications of the equations to take into account the type of cement and the effect of elevated or reduced temperatures on the maturity of the concrete, but this is not discussed here.

3.3 Relief of stress by creep

Figure 9 Reduction over time of re! ,ainedtensile stress due to creep (Curve A early-age contractions, from loo%, curve B shrinkage, from free shrinkage curve C above.).

Some relief of sustained compressive and tensile stresses is provided by creep. Figure 9 shows the reduction over time of both early-age contractions and shrinkage. Early-age contraction stresses are reduced surprisingly rapidly.The figure is based on quite conservative assumptions (loading a t 3.5 days, section 300mm thick exposed on one side only, RH 80%), yet the reduction (curve A) is estimated to be 30% at four months and 60% a t two years. Shrinkage is different. Although each increment of shrinkage is lessened by creep, the shrinkage builds up quite slowly (curve C) so the effect of creep (curve B) is even more delayed. The figure shows that the effect is hardly significant up to one year, although ultimately the reduction is about one-third. 100

90

80 70 60

g 50 40

30 20 10

0 Days 1 Years

2 3

5 7 1014 28

56 100 0.5

1

1000 2 5

10

10,000 20 50

21

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I

Avoid

4. Avoiding cracking or controlling cracking? Concrete cracks when the tensile stress exceeds the tensile strength. Thus the only way to avoid cracking is to ensure that the restraint forces developed within the concrete do not exceed the tensile capacity.

4.1 Avoiding cracking

Cracking can be avoided in two ways: 1. Reduce the restrained contraction sufficiently so that the resulting stress can never exceed the concrete tensile strength. Methods of reducing both the contraction of the concrete and the effect of restraint are discussed below. 2. Introduce an axial compression into the concrete such that any subsequent tensions are not sufficient to exceed the tensile strength of the concrete. An example of this is post-tensioning of ground-bearing or suspended floor slabs.

In many cases option 2 is not practicable as the movements associated with the compression cause further problems, and option 1 is not structurally or architecturally possible. Where this is the case the emphasis must be on controlling cracking through the correct design of the reinforcement.

4.2 CUmUkiVe contractions

The cumulative effect of the different contractions is illustrated in Figure 10.This is drawn for a typical basement ground slab, although the actual tensile stresses a t any point can only be guessed. Line 1 is the tensile strength of the concrete, showing both the strength under transitory stress (la) and the reduced strength (factor 0.7) under sustained stress (Ib); in practice, a value between these two extremes is probably appropriate. Line 2 leading to 2a is the early-age contraction stress, showing the relief from creep (line A in Figure 9). Line 2b shows the addition of long-term drying shrinkage. Crackingwould be triggered if line 2 were to cross line 1. Stresses from neither seasonal nor short-term temperature variations are shown, but it is clear that additional stresses from temperature drop will increase the risk of cracking. However, it is important to note

Figure 10 Tensile strength and stress over time.

4.0

3.0 IT

%

2.0

1.o

0 Days Years

22

0.5

1

2

5

10 20

50

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that if the critical early period of three t o ten days while the concrete is still immature passes without cracks appearing, there is then a ‘honeymoon’ period of months or (more usually) years before the risk reappears in concrete that is by then mature. Furthermore, if the concrete is in a benign environment (such as a water storage tank), the later stresses may never be enough t o exceed the creep relief of the early-age effects. This explains why it is inappropriate t o rely on guidance for water-retaining concrete in the design of basements, see Section 4.3.4.

4.3 Minimum reinforcement in direct tension 4.31 Restrained Structures

4.3.2 Controlling cracking

-

Many structural forms are such that there is no restraint that would cause significant direct tensile stress. This is the case in most superstructures, where a core or shear walls near the centre often provide the stability. However, structures such as basements in contact with the ground, particularly if over about 30m long, tend t o behave as if restrained. These are also structures which often need t o be watertight, or at least waterresisting. The minimum reinforcement in these cases should usually be derived on the assumption that contraction is fully restrained. This is also a sensible precaution if there is doubt about the degree of restraint. The applicability of BS 8007(15) is discussed below.

The principles of controlling cracking by reinforcement are illustrated in Figure 11. If concrete tries t o contract but is restrained so that movement cannot occur, tensile stress gradually builds up. When this reaches the tensile strength of the concrete section, a crack forms. The movement at the crack relieves some of the stress but as the contraction continues, the stress builds up again. If the reinforcement is weaker than the force which caused the first crack, it will yield and all future contraction will be concentrated at the same point so that the crack simply gets wider (Figure Il(a)). If the reinforcement is stronger than the cracking force, it will remain elastic and as the contraction increases a new crack will form at the next weakest cross-section. The process then continues with enough cracks forming to absorb the total contraction (Figure Il(b)), or the cracks are so close together that no further cracks can be formed; this latter situation requires a total strain of around IOOO~E, so is not likely t o be reached under normal movements.The crack in the first model (Figure Il(a)) is uncontrolled while the cracks in the second (Figure Il(b)) are controlled.

Figure I1 Control of cracking by reinforcement.

b. Enough reinforcement

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The amount o f reinforcement t o control cracking, A,, can be derived from first principles by making the strength of the reinforcement, fs,greater than the strength of the concrete in tension, F,.Applying this principle, the reinforced axial capacity is:

and the uncracked capacity is:

where: Ac

area of concrete

E, E,

modulus of elasticity of steel modulus of elasticity of concrete

The second term in brackets is quite small and is neglected at this point, although a correction for i t is applied later. Putting f , 2 F, gives: p 11.0(fc,/f) where:

AsJAc total area of reinforcement, generally equally distributed between t o p and bottom faces.

p A,

Two cases need t o be considered: early-age contractions in immature concrete and total long-term contraction in mature concrete.

4.3.3 lmmatUre Concrete

AppendixA of BS 8007(15)derives a similar expression for pcr1,, the minimum reinforcement ratio for the early thermal contraction case:

where: direct tensile strength of the immature concrete, usually taken at the age of three days as 1.6MPa for C28/35A concrete.

f,,

Hughes(17)explains that f,, includes a hidden y,

= 11,

and quotes a more general value:

where:

f,, with

24

28-day cube strength = 460MPa,

P,,,~= 1.6/460 = 0.35%,the familiar value in BS 8007.

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Serviceability calculations are normally carried out on mean values; however, controlling restraint cracking should not necessarily be thought of as in the same category as most other serviceability criteria. Mean values imply that some will be better and some will be worse, but crack control is fundamental to the satisfactory behaviour of structures such as basements and an uncontrolled crack could have significant consequences.Therefore the rest of this section is formulated with the aim of achieving a 95% limit, i.e. only 1 in 20 failures. Lower amounts of reinforcement may be appropriate where the consequences of an uncontrolled crack are less serious. BS EN 1992-1-1 quotes the lower and upper characteristic tensile strengths of concrete as O.7fc,, and 1.3fct,. Part of this range relates to the variation between different concretes of the same specified strength but part of it relates to the variation between samples from

the same concrete. In a long structure the weakest concrete will crack first (i.e.the weakest sample); similarly, stress concentrations will initiate cracks a t average stresses significantly lower than the tensile strength. While it is not possible to quantify these things exactly, a value of l.O[,, might be appropriate for a long slab with various discontinuities such as columns, walls and small holes, while 1.3fct, might be more appropriatefor a basement floor restrained a t close intervals by pile caps. It is also sensible to allow not for the specified minimum concrete strength but for the average. BS EN 1992-1-1allows for a strength 8/10MPa (cylinder/cube) above that specified as the mean value, although a higher strength may be delivered for other reasons, e.g. early striking of formwork or concretes with fly ash or ggbs which gain strength more slowly, in which case ,f should be based on this higher strength.

If the maximum concrete tensile strength is combined with the minimum reinforcement yield strength, the resulting probability is 1 in 20 x 20, i.e. 1 in 400. This is not what is intended, and the I-in-20 overall probability is achieved by combining the maximum concrete tensile strength with the mean reinforcement strength. Since January2006, the characteristic reinforcement strength has been 500MPa with the mean expected to be approximately 550MPa, so if we wish to retain the characteristic reinforcement strength in the formula a correction factor of 500/550 needs to be introduced.The other correction introduced is 1.06 for the enhancement of tensile strength F, given by 0.6% reinforcement. This leads to the minimum reinforcement content for immature concrete of:

P,,,~= [(1.0to 1.3) x 1.06 x (500/550)] (fCt,,,,/tk), which approximates to: 1.00 to 1.25 (f,,,,mm/fyk)

(note BS EN 1992-1-1 would give 1.00)

BS EN 1992-1-1gives the tensile strength of concrete before 28 days as:

where: 5

0.2 for Class R cements 0.25 for Class N and 0.38 for Class S

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If it is assumed that the critical value for f,,,,,, occurs a t three days and Class R cements are used then:

Values of f,,,,,,

and p,,,, for a range of concrete strengths are shown in Table 7.It can be

seen that for all normal structural concrete classes, values are higher than the BS 8007 value of 0.35%. Having controlled the cracking with this minimum amount, more reinforcement may need to be added to achieve a desired crack width, see Chapter 9. Table 7 Minimum reinforcement contents in direct tension for immature concrete related to strength class (total in both faces).

4.3.4 Mature concrete

Immaturetensile strength, j,,,,, (MPa)

1.45

1.85

2.1

2.5

P,,,, = 1.0 Vct,,mm/fyk) ("/I

0.29

0.37

0.42

0.50

PCli,= 1.25 cVct,i,~fyk)

0.36

0.46

0.53

0.63

(%)

Although referenced by documents such as BS 8102(16BS ),8007cannot be relied on for designing basements to be watertight. BS 8007is written for reservoirs, i.e. concrete tanks which in service will be full of water and usually embedded in soil, often with a covering of soil on the roof. In these conditions, shrinkage is minimal and temperature variations small. BS 8007assumes that if early-age contractions are controlled, subsequent movements will be insignificant,or a t least less than the reduction from creep (although this is not stated). In basements the internal faces are open to the atmosphere and therefore shrinkage will occur. Temperature variations may also need to be considered.The worst case is basements used for car parking, especially if they are naturally ventilated, as the concrete is then exposed to near-ambient temperature and humidity all year round. However for mature concrete a further adjustment to the calculation above should be made. Under sustained loading, the tensile strength of concrete is understood to reduce by around 0.7. The dominant cause of full-depth cracking is sustained contraction (long-term shrinkage and seasonal temperature drops added to early-age contractions) although more rapid temperature drops frequently contribute. Allocating these %:% suggests that a reduction in f,,, for long-term effects of 0.8 can be applied. Taking this into account, the minimum reinforcement content for mature concrete is: p',,,,z (0.8 to 1.0) fctm/Sk

(BS EN 1992-1-1 uses 1.0; this is recommended)

where the prime (') is used to refer to mature concrete to distinguish it from the immature stage.

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This results in the minimum percentages in the bottom row of Table 8. A comparison can be made with the design of continuous reinforced concrete pavements, for which the Highways Agency specifies 0.6% reinforcement in a single layer at the mid-depth. Table 8 Minimum tension strength reinforcement for mature class (total concrete contents in both related infaces). direct to

,-

.

y o l y i m e ,

.

Mean mature tensile strength,fctm(MPa)

22

28

32

38

P’,,,, = 1.00 V,,,~r,,, (“b)

0 44

0.56

0.64

0.76

BS EN 1992-1-1 makes an allowance in slabs over 300mm thick for ‘non-uniform selfequilibrating stresses’ (i.e. a balance between high shrinkage near the surface and much lower shrinkage in the interior).This is expressed as a multiplier ranging from 1.0 a t h = 300mm down to 0.65 a t h = 800mm and over. This can also be thought of as defining surface zones with thickness increasing from 150rnm a t h = 300mm to 260mm a t h = 800mm and 0.325h a t higher values of h; these can be compared with the zones defined in Figure A2 of BS 8007 (hl2 up to h = 500mm and Z50mm beyond that). Figure 12 compares the approaches in BS 8007 and BS EN 1992-1-1; it is recommendedthat the guidance in BS EN 1992-1-1 is followed. Figure 12 Comparison of surface zones in BS 8007 and BS EN 1992-1-1.

1.0 0.9 -

0.8 0.7 0.6 0.5

\ \

\ ..

.------________ -- BS EN 1992-1-1 \

8s 8007

600 300

E

E

o

300 300

I

h

600

4.3.5 FlOW chart

The analysis above for elements subject to direct tension has been consolidated into a flow chart (see Figure 13).Working down from the top, stage 1 deals with early-age contractions, stage 2 covers the relatively rapid increase of compressive and tensile strength, and stage 3 describes the subsequent behaviour of the mature concrete.The immature strength of the concrete is denoted as fct,and the mature strength Ct2. The stresses a t the corresponding stages are uct,and uctr. In order to remain uncracked, the tensile strength must exceed both the tensile stress in the immature phase and the accumulation of tensile stresses when the concrete is mature. Unless there is very little restraint and care is taken to limit contraction throughout the life of the concrete, cracking is likely, so that it is preferable to assume that cracking will occur

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and provide sufficient reinforcement t o control it. The flow chart emphasises that, unless the tensile stress in the mature concrete can be assured t o remain below the tensile strength, reinforcement t o control cracking must be based on the strength of the mature concrete. The key area not properly dealt with in any code of practice or industry-standard publication is where p is greater than p,,,, but less than pLrl,.Then the cracks that were controlled for early-age contractions become uncontrolled for all further contraction movements. Providing sufficient cracks have opened during the early-age contractions, although they

will grow beyond their design values, the consequences may be minor. If however there is little early age cracking, all the subsequent crack movement could be concentrated in one or two cracks, leading t o much larger crack widths. If p is greater than pkr,,,new cracks form in addition t o the original ones and both old and new cracks are controlled. It is also clear that if the amount of reinforcement is insufficient t o control cracking, whatever is provided is wasted as it achieves nothing - a classic case of false economy

The flow chart can also be used by an observer examining cracks for the first time. O f the three different outcomes two are straightforward: a uniform pattern of controlled cracks or a random array of uncontrolled cracks. The unusual one is the uniform pattern of initially controlled cracks which have later become uncontrolled, the result of p being greater than P,,,~but less than p;rlt. An example of this is described and illustrated in Chapter 11. Figure 13

START

Flow chart showing possibleoutcomes in restrained sections subject to linear tensile stress.

i ‘

No

15 act1 > f C t l ?

Yes

1s P 2 Pcrit’

No

I

Yes 7

Sections remain uncracked

Multiple controlled cracks form

___________________________ Stage few weeks

Random wide uncontrolled cracks

I

____________________--------

Compressive and tensile strengths increase

I

remain ;(in additior unaffected t o any I existing j cracks)

;

20

Uncontrolled existing cracks become wider

Incontrolled:jUncontrolled new j existing random random wide j cracks cracks j become wider form ~

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5. Internal restraint Internal restraint may be provided by the reinforcement. This can resist shortening of the concrete and occasionally leads t o cracking. If the reinforcement is asymmetrical it will lead t o deflection.

5.1Res,,aint by reinforcement - symmetrical sections

51 1 Restrained shortening

The restraining effect of reinforcement can best be visualised by considering a length of say I m taken from a column and imagining first that the reinforcement is disconnected from the concrete, for example by being greased. When the shrinkage takes place, the ends of the reinforcement will be left projecting from the face. If the reinforcement is then pushed back into the concrete and at the same time the concrete is pulled out so that the surface is flush once again, this models the restraining effect of the reinforcement (see Figure 14).

Figure 14 F = E, E,A,

Representation of shrinkage restrained by symmetrical reinforcement.

a. Before shrinkage

b. After unrestrained c. Shrinkage restrained shrinkage by reinforcement

This gives the restrained shrinkage as:

where: ae E,,

P

modular ratio €)Eeff where Eettisas defined in Section 3.2 unrestrained (free) shrinkage reinforcement ratio A)Ac

This looks simple, but how is cp t o be evaluated when the shrinkage is progressive throughout the life of the structure and each increment is subsequently relieved by creep? Examination by a spreadsheet which applies the shrinkage in a number of stages suggests that the equivalent result is obtained by applying the whole shrinkage at an age of 150 days and calculating cp accordingly. Reassuringly, the result differs insignificantly over a considerable variation in this age.

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ical structure indoors (RH = 45%, concret = 11.SCPa and a,= 17.5. Some values of a, calculated in this es inTable 7.2 of BS 8110-2 are t o Table 9, which suggests that t h Table 9

Concrete ttnngth class

Envinmmant

32/47

0,=17

75/85

a, = 10

Values of modular ratio a, for concretes in indoor and outdoor environments.

51.2 Tensile Stress

Remember that although reinforcement reduces the contraction, it is at the penalty of tension in the concrete. The average tensik stress can be calculated from.

As an example, the 30-year tensile stress from 3 0 0 of~ shrinkage ~ in CO

Wall in Piccadilly Gardens, Man&Wr.

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Figure 16 Representation of shrinkage restrained by asymmetrical reinforcement.

a. Before shrinkage

b. After unrestrained shrinkage

ECS

c. Shrinkage restrained by reinforcement

5.2 Restraint by reinforcement asymmetrica1 sections 5.21 Curvature and deflection

Unlike columns, beams and slabs are usually reinforced more heavily in the bottom than the t o p at mid-span and vice versa over the supports, and the resulting asymmetry of restraint causes curvature which leads t o deflection. If we again imagine a length with the reinforcement disconnected from the concrete (see Figure 16(a)), shrinkage of the concrete will then leave the reinforcement projecting from the free end (Figure 16(b)). If the concrete is then pulled out and the reinforcement compressed so that the ends are once again flush, the stresses and strains induced are those caused by the restraint (Figure 16(c)). The strain E~ in the reinforcement is used t o define the force, and the stress in the concrete is calculated by the conventional formula FIA + My/I. The resulting strain at the level of reinforcement is equated t o ( E , ~- E ) , giving the following formula for the uncracked shrinkage curvature:

where: Ecs ae

E,,,

p 5 8

I,

rg

free shrinkage strain modular ratio €SI€,, effective modulus of elasticity of the concrete; the creep coefficient cp can be calculated assuming the shrinkage occurs at 150 days (as explained in Section 5.1 .1 above) ratio A,IAc of reinforcement area t o concrete section net first moment of area of the reinforcement about the neutral axis of the concrete section (i.e. deducting 5 of any compression reinforcement) second moment of area of the concrete section second moment of area of the gross cross-section, calculated as

Ic+ (ae- 1) I [ A 8( d - ~ , ) ~where ] , xc is the depth t o the centroid of the concrete section

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The deflection 6 is then given by:

6= 0125~~,,l* where:

L

span

The coefficient 0.125 is replaced by 0.5 for a cantilever, and can be adjusted for continuity at the supports by the method of BS 8110 - 2 Table 3.1. Guidance on shrinkage deflection in cracked sections is given in BS EN 1992-1-1, although BS 5400-4(’*) and American guidance both recommend significantly lower deflections; this is discussed by Alexander(lg).Research currently being undertaken at Durham University (2007-2008) aims t o resolve the difference.

5.2.2Tensile Stress

The ‘locked-in’ tensile stress at the extreme fibre from curvature is:

where: xg

depth t o the centroid of the gross cross-section

and using the same E,,, as used t o calculate

K~,,

The total tensile stress is the sum uct,+ ucct2. In the long term, this can be significant, typically ranging from 0.3 t o 1.2MPa as the reinforcement increases from 0.25 t o 1.0%. It appears t o be overlooked in codes of practice when ascertaining whether the section is cracked under load. Estimating shrinkage effects at intermediate ages is not easy. One way is t o recognise that shrinkage curvature is only a small contribution t o the total curvature and t o make an educated guess. It is also possible t o set up a spreadsheet that divides the shrinkage into increments which add up t o the total curvature at the point in time required.

5.3Temperature differentials

Another form of internal restraint is that caused by differential strains within the concrete. For example it is known that as the concrete dries from the outside, more shrinkage occurs t o the skin which is restrained by the core. In sections over about 5 0 0 m m thick, this can cause surface cracking. A more significant effect is that of differential temperature distribution, for example where

solar radiation raises the temperature of the top surface of a bridge or car park deck. In principle if one side of an element heats, it tries t o expand, so if it is restrained by the rest o f the element, curvature is induced. If the temperature profile across the element is linear

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and there are n o other restraints, the curvature can be calculated simply from the temperature difference and the thermal coefficient of expansion for the concrete. However, in reality, due t o the effects of solar radiation and the thermal mass of the element, linear temperature distributions are often not achieved. Further information on the variation of temperature through elements can be found in BS 5400-2(12). Temperature differentials are only normally significant for structures directly exposed t o the environment and particularly t o direct solar radiation. A typical structure that may be exposed in this way is a multi-storey car park.This is discussed in more detail in Section 11.4.

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6. Surface restraint Casting an in-situ concrete topping onto a precast concrete substrate or base unit is a common way of forming a homogeneousslab. Many types of hybrid construction are also formed in the same basic way. However, the contraction of the topping (arisingfrom earlyage contractions and long-term drying shrinkage) produces internal stresses which lead to shortening and deflection of the composite unit, and sometimes to cracking in the topping. The same theory can be applied when the base unit is prestressed although composite steel-concrete sections are considered in Section 6.2. This section explains the theory and shows how to calculate the effects. A numerical example and a case study are presented in Appendix A2.

6.1 In-situ toppings 611 Method of analysis

Consider a topping cast onto a base section (Figure 17(a)),and firstly allow the contraction of the topping to take place freely, as if the interface is greased (Figure 17(b)).Thenapply a tensile force fl acting a t the centroid of the topping so that the relative movement at the interface is eliminated (Figure 17(c)). At this point the topping and the base are joined to form a composite section, and finally an equal and opposite force f , is applied to the composite section (Figure 17(d)).

Figure 17

Contraction of in situ toppings

Contraction of in-situ concrete.

L a. Before contraction

f

T

r

F

l

I&

b. After unrestrained contraction

T7TF2

_ _ _ _ I __:_

_. c. Force F, t o overcome contraction

___ d. Force F2 on composite section

The stresses in the topping are the sum of the effects of forces F, and F,, giving the expected tension. This can be calculated as o, + U, where:

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where:

-F, = E, E, Aa

F,

=

E,, E~

contraction of topping and base in same time period

En

net contraction = E,

aab

‘,IE,

-E,

where: Ea effective elastic modulus of topping

Aa

e y Ag

4

E, effective elastic modulus of base transformed area of topping (i.e. allowing for any reinforcement) distance between centroid of transformed topping and centroid of transformed composite section distance between required stress location and centroid of transformed composite section transformed area of composite section transformed moment of inertia of composite section

The properties of the composite section should take into account the extent t o which it is (or may become) cracked.

61.2Curvature and deflection

The curvature is obtained from the generic formula M/EL that is:

The deflection 6 is then given by:

6= 0.125~L’ where: L span, assumed simply supported, i.e. ignoring any continuity a t the supports. The coefficient 0.125is replaced by 0.5 for a cantilever. Note that the method can be used over any period of time. For instance, the effects of early-age contractions are virtually immediate, so that short-term values would be used t o give the immediate stresses, curvature and deflection. Long-term values can be used t o give the long-term effect, although splitting the behaviour into three or more time intervals with a spreadsheet will be more accurate as F will decline with time. The same spreadsheet approach may be necessary t o find the point at which E, overtakes E, if the base is prestressed.

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6.2 Composite slabs on steel decking 6.21 Method O f analysis

Concrete shrinks but steel does not, so in composite construction shrinkage contraction of the in-situ concrete slab induces deflection in the composite section. More importantly, composite floors are prone to cracking. Due to the fact that most floors are covered by a raised floor or other finishes, cracks on the top surface are not normally visible, and the metal deck means that cracks are also not visible from below. However, if the slab is left uncovered, and especially if it is finished smooth, any cracking can become a significant problem. Cracking can be largely explained by the contraction of the concrete. For simplicity, the scope of this section is limited to simply supported beams in buildings in indoor conditions. The form of restraint is very similar to that in the previous section and the calculation using the principle of superposition is explained diagrammatically in Figure 18

Figure 18 Contraction of in-situ concrete slab on steel beam.

I

f

U a. Before contraction

T

m

r

F

l

f b. After unrestrained contraction

T

T

\

-

j

Z

--

c. Force F, t o overcome contraction

2

- -- -- -- r

d. Force f , on composite section

The concrete slab is allowed to contract independently of the steel beam as before. A force F, is applied at the centroid of the slab to stretch it back to its original position (Figure 18(c)). At this point, the slab is ‘glued’ to the beam to form a composite section. An equal and opposite force F2 acting at the centroid of the slab is now applied to the composite section (Figure 18(d)). The stresses in the slab are the sum of the effects of forces F, and F2, giving the expected tension. This can be calculated as U, + a2where:

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where:

4

= -F, = E,,

E, Aa

contraction of slab in time period considered (reduced for internal restraint o f reinforcement and metal deck) at-

ESIEC

Ac

where: fc effective elastic modulus of transformed slab E, elastic modulus of steel transformed area of slab (i.e. allowing for reinforcement and metal deck) distance between centroid of transformed slab and centroid of transformed composite section distance between required stress location and centroid of transformed

e y A,

I,

composite section transformed area of composite section transformed moment of inertia of composite section

There are t w o potential sources of contraction: early-age contractions and long-term drying shrinkage. Temperature variations can usually be assumed t o affect the concrete and the steel equally. In composite slabs the heat of hydration can escape from both the top and bottom surfaces of what is a relatively thin member and so the early thermal temperature rise will be very small - a few degrees at most. Autogenous shrinkage and other early shrinkage effects are discussed in Chapter 2. For the strength classes of concrete commonly used in composite slabs, a small allowance should cover most situations, including using lightweight aggregate concrete. This suggests that a nominal overall allowance of say 1 5 0 p will be appropriate for early-age contractions. As the steel beam provides virtually full restraint, this can then be reduced by 50% for creep, i.e. t o 7 5 p . At this point some assumptions need t o be clarified. The first is that because the metal decking is bonded continuously t o the concrete, i t can be treated in the same way as embedded reinforcement. Also, because the slab is attached t o the steel beam which forces it t o contract linearly it does n o t matter whether the decking (or for that matter the reinforcement) is not concentric in the section. For typical slab profiles with steel decking 0.9-1.2mm thick and A142 fabric reinforcement, p ranges from 1.0 t o 1.4%. Section 2.3 goes on t o show that the shrinkage occurs continuously, that each increment is subsequently relieved by creep, and that this can be modelled by applying the total shrinkage in one step at age 150 days. This gives a typical value of the modular ratio a, of 17.5. Thus the effect of the internal restraint is a factor of 0.80-0.85.

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6.2.2 Curvature and deflection

The curvature is obtained from the generic formula M/€I, that is: K = F,

=

e I E, I g Ac e I a, Ig

The Steel De~igners’Manual(~’) adapts this so as t o be expressed in terms of more familiar parameters (see Figure 19): K=

(D + D, + DP) AS/ [2 (1 + a,p) Ip]

Figure 19 Notation used in Steel Designers’ManuaL

The deflection 6 is then given by:

6 = O.l25~1* where: span, assumed simply supported, i.e. ignoring any continuity at the supports L

6.2.3 Codes and standards

BS EN 1994-1-1(2’)states that:

“Unless specifically required by the client, the effect of curvature due t o shrinkage of concrete need not be included when the ratio of span t o overall depth of the beam is not greater than 20.”

The risk of cracking in the slab is not specifically mentioned

6.2.4 Conclusions deflect ion

Parametric studies suggest that the shrinkage deflection can be significant, and should probably be included as part of the total long-term deflection. Interestingly, shrinkage acts on the shear connectors in the opposite direction t o applied loading, which suggests that increasing load deflection for partial shear connection is over-conservative, A simple rule would be t o assume shrinkage deflection is equal t o span11000 unless it is estimated by a more accurate calculation, in spite of the let-off in BS EN 1994-1-1.

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6.2.5 COnClUSiOnS - cracking in the slab

Tensile stress is induced in the slab in four ways. First is the internal restraint of the reinforcement and the metal deck.Taking typical long-term values of and ae= 17.5 gives = 0.7 to 0.9MPa for p = 1.0 to1.4%.

ttl

= 400p, Eb= 200CPa

Second is the restraint of the steel beam itself.This produces a tensile stress a t the centroid of the slab = u1+ o2as defined in Section 6.31. This varies with the size of the steel section but is typically from 0.25MPa for a shallow light section to 0.9MPa for a deep heavy section. Third is the restraint of the surrounding structure. This will usually be a t least O.25MPa. This suggests that the resulting tensile stress will be at least 1.2MPa and could be over 2.OMPa. However, these are mean values and ignore the fourth factor: the differential caused by the concrete near the top drying out faster than the concrete near the bottom (which will dry slowly owing to the metal deck). If the concrete adjacent to the metal deck did not shrink a t all, these values could double a t the surface. While the effect in the early months might be close to this, in the critical period around one to three years the ratio will probably drop to around 1.25 to 1.5. Assuming 85% of the final shrinkage has occurred by this time, this effect will increase the values above to at least 1.3MPa and as much as 2.6MPa. All of the above assumes that the deck is acting in a simply supported manner and this is normally the design assumption; however, the slab is continuous, normally in both directions

and this will induce further tension in the hogging zones. For the strength classes of concrete normally used in composite construction, the tensile strength of concrete under sustained loading is probably in the range 1.5-2.25MPa. It is clear that the possibility of the concrete cracking is very real and should be considered, particularly where composite slabs are to be left exposed to view. This is endorsed in Concrete Society Concrete Advice Sheet 13(22). Cracking could theoretically be controlled by providing a minimum reinforcement content in accordance with Section 4.3. It might be thought that the metal deck would perform this function, at least a t right angles to the corrugations, but evidence from sites suggests otherwise.

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7. Edge restraint This document splits external restraint into two cases Edge restraint and Endrestraint (see Chapter 8).These two types of restraint are really limiting forms of restraint. In practice, the situation is somewhat more complicated and the actual restraint is either a combination of these two forms or, more likely when early thermal movements are being considered, one of edge restraint. This is inconsistent with the basic structural model from which the British and European approaches are derived which is one of a member restrained at its ends against overall shortening. Figure 20 illustrates the two forms of restraint. Figure 20 End and edge restraint.

a. Restraint of a wall at its ends

b. Restraint along one edge

An example of where both forms of restraint exist can be found by considering a new section of concrete cast between two pre-existing concrete wall sections and onto a preexisting concrete base. At the base, edge restraint will dominate (see Figure 21). However, further up the wall away from the base, edge restraint will become less significant and end restraint will become more influential. At a point within the height of the wall, end restraint will dominate and edge restraint becomes insignificant. The position and significance of the two restraint conditions is obviously dependent on the height, cross-section and length of the concrete section as well as the concrete base. Figure 21 Approximate regions of domination of end (zone 1) and edge (zone 2) restraint in an infill wall.

, Zone 1 _ / _ _ - - - - - - - - _ _ _ _

Zone 2

End restraint, which has been researched extensively over the last 30 years and is reasonably well understood, will be considered in Chapter 8. The current section will concentrate only on edge (base) restraint which in comparison has been studied very little. In fact only two investigations can be cited where base restraint has been researched, namely AI Rawi and Khede~(*~) and S t ~ f f e r s ( ~Unfortunately ~). the experimental materials, approach and scarcity of reported information mean it is difficult draw any meaningful conclusions from these investigations.

7.1 Control O f cracking

40

This section considers edge restraint in terms of its influence on cracking and the size of the cracks (crack widths) and the effects it will have on the design and detailing of the cross-section in terms of the steel reinforcement it uses t o control cracking and crack widths.

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With end restraint conditions, the crack width will depend on the tensile strength of the concrete. For edge-restrained situations, the crack width depends on the restrained imposed strain and not the tensile strength of the concrete. The amwnt of horizontal reinforcement is ed to control both early thermal cracking (restraintto early thermal movement), and in some situations such as a thin slab cast against an existing massive differentialshrinkage and in-use temperature movements. about 0.2% of anti-crack reinforcement whereas BS 8007(15) requires nearly twice this amount (because of the intended use of the structure and the better control of crack widths required in water-retaining structures).The Eurocodes require between 0.3 and OS%, see Chapter 4. These all relate to restraint of early thermal movement based on end-restraint condition and not edge restraint.The question is one of whether this amount of steel is actually necessary. ifferent from those in endFactors which influence cracking in base-restrained w llwill crack and the size of restrained sections. Consider first the way a base-rest the crack widths Figure 22 illustrates the conditions in a wall after initial cracking.

Figure 22 Conditionsin a base-restrainedwall after initial cracking.

Initially consider a wall completely restrained along its base and with no reinforcement. Once sufficient contraction has occurred, cracks will form. At the primary crack (which will be the full height of the wall) the stress in the concrete is zero. However, with increasing distance from the crack, stress is transferred to the wall by shear at the interfacewith the base until, at some distance I, from the crack, the stress distribution is unaffected by the crack. In the end-restrained case (Chapter 8),the crack reduces the stiffness of the whole system and hence reduces the stresses throughout. This is fundamentally different from the edge-restrained case considered here where the relief of stress caused by the crack is k and further cracks may purely local. Stresses are not relieved beyond I, from the form in the unrelieved areas. These cracks will have no influence on the first crack. Figure 23 illustrates a simplified version of the poTential cracking behaviour i adjacent to the primary crack as concluded by A1 Rawi and KhedeP).They found that the stress relief provided by the crack varied throughout the height of the wall, being much greater at the top of the wall than at the base.

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I

Figure 23 Cracking adjacent t o a primary crack (from A1 Rawi and Kheder("1).

Referring to Figure 23: 0

Zone A. No further cracks will occur within this zone.

0 Zone

0

B. No new cracks will initiate within this zone but cracks initiating in zone C may

pass into zone B. These cracks will generally be relatively small, reducingto zero width on reaching the boundary of zone A. Zone C. New cracks may initiate within this zone as the stresses in the concrete are only minimally relieved by the primary crack. If a crack forms beyond 2H from the primary crack, the new crack will be a primary crack. If the crack forms a t a distance less than 2H from the primary crack, the crack will reach a maximum width close to the boundary with zone B. If the crack reaches zone A, the width a t this point will be zero. If the crack lies a t a distance greater than H from the primary crack, it will reach the top of the wall but the width will be relatively small and certainly not greater than the width at the zone B-C boundary. Thus, though more cracks may form, the cracks initiating in zone C will not significantly affect the width of the primary crack, which will remain the largest crack and therefore the critical crack from the design point of view.

This variation in stress relief through the height of a wall was also found by Beeby and Forth(2S) who carried out a finite-element analysis to assess the width of a crack for a given strain and also looked a t the influence of secondary cracking in areas away from the primary crack (in equivalent zones to C and B above).The elastic analysis was performed on an idealised structure as shown in Figure 24. The unreinforced wall dimensions of I m high by 10m long were chosen to ensure that the deformations and stresses near the free vertical end were independent of the wall length. Initially, the crack width for a wall without any secondary cracking was considered. Figure 24 Analytical model of wall on rigid base. Location of 'crack' I t

I I I

Axis of symmetry - no deformation

Fixed base - no deformation in x ory direction along this line

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As the material is assumed t o be elastic, the deformations will scale and therefore the

deformations of the free vertical end (equivalent t o half the crack width) will be proportional t o the height of the wall and the imposed strain, \

Figure 25 illustrates the primary crack widths calculated a t the free end of the baserestrained wall. In addition, the influence of secondary cracks on the primary crack width, located at a distance of 1.2H from the primary crack, was considered in the analyses.These cracks had a height of 0.4H, 0.6H and 0.8H. Figure 26 shows the widths of the primary crack and the secondary cracks for these cases as well as the case of no secondary crack. It will be seen, first, that the secondary cracks have minimal effect on the widths of the primary crack and, second, that the widths of the secondary cracks are always smaller than the primary crack. This suggests the tentative conclusion that, from the design point of view, only the primary crack needs t o be considered and that the width of the primary crack can be calculated ignoring the presence of any secondary cracking. Figure 25 Primary cracks calculated at the free end.

0

0.5

1

1.5

2

2.5

3

wI(EimpH)

Now consider what happens when horizontal reinforcement is provided in the wall. From the discussion above, it will be seen that it is only necessary t o consider the primary cracks. The effect of reinforcement must be t o improve the transfer of stress t o the concrete with increasing distance from the crack and thus t o reduce the crack width to below that obtained for the situation with no reinforcement. It will also provide a force across the free end surface which will act t o reduce the deformations below that calculated for zero reinforcement. Using the finite-element model described above, the reinforcement can be modelled by springs applied at the face of the ‘crack’. The stiffness of these springs may be estimated by assuming a transfer length over which force is transferred t o the concrete from the bars with a uniform bond stress over the transfer length. Two possibilities were considered: first BS EN 1992-1-1[’) which gives: L,

=1

. 7 +~ 0.17# /pp,eff

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and second, a paper by Beeby and Scott(26) which gives:

I, = 3c where: cover bar diameter pp,efi effective reinforcement content C

It is less easy to produce parameterisedvalues of crack widths in this case and analyses were carried out for a 1000mm high wall reinforced with bars at 250mm centres in both faces with a cover of 35mm. An imposed strain of 100 x 10-6was applied and the elastic modulus of the concrete allowing for creep was assumed to be 14CPa.Various bar sizes were considered and Figure 26 shows the calculated crack widths at the position of the topmost bar for each bar size calculated using the crack width formulae in BS EN 1992-1-1 and Beeby and Scott to estimate the spring stiffnesses. Figure 26 Effect of reinforcement content on maximum crack width.

3.5 3 2.5 F - 2 ._ E 5 3 1.5 1

0.5 0

These calculations show that the effect of reinforcement is considerable, as one would expect. The sensitivity of the results to the relationship chosen for L, is interesting. BS EN 1992-1-1gives substantially greater lengths for L, than Beeby and Scott and hence much lower spring stiffnesses.This leads to roughly halving the influence of the reinforcement on the crack width and a very much lower steel stress. The two relationshipsare compared with data obtained by S t o f f e r ~ (in~ Figure ~) 26. So far only the case where the base is completely rigid has been considered. However, this

is unlikely in practice as a base will not provide total restraint of the type assumed in the analysis. Two effects become apparent once it is assumed that the base is not completely rigid. First, the shortening of the wall will lead to some contraction of the base. This can as the difference between the easily be dealt with by considering the restrained strain, free strain that the wall would have achieved if unrestrained and the strain that it did achieve, in this case the shortening of the base.

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Second, a more complex effect will arise. Shortening of the wall relative t o the base will result in an in-plane moment in the combined wall and base which will try t o lift up the ends of the wall. This will result in the stresses and strains in the wall being rather different from those calculated. In fact, the top of the wall will shorten rather more than the analysis above will suggest, resulting in larger primary cracks. An analysis of a complete wall plus a base supported on soil was carried out t o gain an impression of the likely effect.The analysis did indeed result in substantially larger primary cracks where the wall was unreinforced but the effect of reinforcement in reducing the crack width is more dramatic than in the cases where in-plane curvature is not modelled. This is a complex problem which needs further extensive analysis. Stoffers considered this problem both theoretically and with three wall tests. His results also show an increase in primary crack widths.

7.2 Restrained strain

From the mechanisms discussed in Section 71 i t will be seen that the calculation o f the is required t o calculate the likely crack width. In practical terms this restrained movement is calculated by multiplying the free strain by a restraint factor Rax.Annex L of BS EN 1992-3 provides values for the value of Raxfor typical conditions of restraint. A value of Rax= 1 corresponds t o total restraint and Rax= 0 corresponds t o zero restraint. As Raxincreases then the crack width also increases; for example, if Rax= 0 the movement is totally unrestrained and therefore no stresses develop and so likewise no cracking.

7.3 Summary

Many of the comments presented in this section are based on a finite-element analysis and, where possible, findings were validated with current theories and practice as well as by reference t o the work by AI Rawi and Kheder(23)and S t ~ f f e r s i ~It~is) .clear that crack widths in edge-restrained walls are proportional t o the imposed strain whereas crack widths in end-restrained walls are proportional t o the tensile strength of the concrete. It appears that with practical amounts o f reinforcement, steel stresses and crack widths are likely t o be smaller for edge restraint than for end restraint. Further, the lower steel stresses could suggest that the concept of minimum steel percentage t o avoid yield of the steel on first cracking is not applicable t o edge-restrained conditions. However, for many elements some zones will be subject t o end restraint and others t o edge restraint; in addition, elements that initially have edge restraint due t o early thermal movements will eventually develop end restraint due t o long-term shrinkage. lit is therefore recommended that the minimum steel t o prevent yield at first crack is always provided, although where edge restraint is clearly dominant the calculation of crack width should take this into account (see Chapter 9).

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I

8. End restraint There are two commonly occurring applications of end restraint: superstructure slabs between widely spaced cores or shear walls; and basement floor slabs between piles or pile caps - o r even restrained by friction with the soil. As explained in Chapter 7, portions of edge-restrained walls and slabs which are remote from the restrained edge also tend t o behave as end restrained, and it is conservative t o treat them in this way.

8.1 Minimum reitlfOrCe~etlt

8.2 Superstructure slabs 8.21 Spacing O f movement joints

The explanation of cracking and derivation of minimum reinforcement given in Chapter 4 relates principally t o end restraint. It is important t o recognise that all theories of endrestraint behaviour make the assumption that the reinforcement is acting in its elastic range, and that for this t o be true the minimum content derived in Chapter 4 must be provided.

In the past reinforced concrete floor plates tended t o be regular beam-and-slab structures, and good practice and rules of thumb indicated that if movement joints were provided not more than 30-40m apart, cracking could be controlled. Flab slab construction, often in a free-form layout, has become the norm. This factor, combined with the desire by engineers and architects t o avoid movement joints due t o complications with finishes, appearance and stability, has led t o more ambitious spacing of movement joints. Lengths of 80m between movement joints are now not unusual. This desire t o eliminate movement joints has been met with varying degrees of success. Slabs up t o 70-80m long have been cast without any signs of undue stress, while other slabs even less than 30m long have cracked. A review of the main reasons for success has shown some consistent factors, which are in a way self-evident, as follows: 1. The slabs are reinforced uniformly and usually with reinforcement above the values previously adopted. 2. The columns are small and flexible and offer little restraint t o lateral movement. 3. The slabs are properly cured. 4. Construction joints are carefully planned t o eliminate areas of stress concentration and t o limit the size of pours. 5. In summer, large areas of slab are avoided or are protected from sudden temperature drops a t night. 6. Careful mix design in terms of selection of appropriate aggregates and cement types has been adopted.

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.... .. ....

..- -

..

___ -. .

... __ .

.

.

The structures most at risk are open car parks, structures cast in the summer, lightly reinforced slabs, structures with stiff columns or shear walls, and slabs with atria or large holes or other sudden changes in plan form. In addition, this includes structures where the strength of concrete has greatly exceeded the design strength resulting in an increase in tensile capacity of the concrete and therefore insufficient reinforcement t o comply with As,,,,,,,. Over recent years a greater understanding of both early-age and shrinkage cracking has been developed. Much of the early work (e.g. by hug he^(*^)) was concentrated on early thermal contraction as this was a serious problem for leak-resistant water storage structures. Early thermal cracking of thick walls and basement slabs greater than 500mm thick was also carefully researched by Bamforth(28)and others. Early thermal shrinkage of slabs was clarified and explained by the Reinforced Concrete Council in large areapoursfors~spendedslabs(~~). This document pulled together the current thinking into a workable form for engineers t o apply t o designs. More recently ClRlA Report C660 Earlyage thermal crack control in concretei5)has been published, which updates the current research and recommendations for design. However, the concentration of effort into the important topic of early thermal cracking has meant that long-term shrinkage cracking has tended t o be overlooked. This has not been a serious omission provided that movement joints were located following good practice, i.e. 30-40m spacing. This section looks at some of the implications of large floor plates and discusses methods of checking the effects of long-term shrinkage in conjunction with expansion or contraction due t o temperature effects.

8.2.2Design methods

,

.

Various methodologies have been suggested for the behaviour of restrained slabs. The Reinforced Concrete Council publication large area poursf~rsuspendedslabs(~~) adopted the concept of a restraint factor R t o modify the effect of early-age contractions. Similar factors for restraint have also been adopted in PD 6687t30),the background paper t o the UK National Annexes t o BS EN 1992-1-1. The following method, which has been developed using the principles of BS EN 1992-1-1(’) and BS EN 1992-31’1, takes the basic formulae for crack width and spacing t o build them into a coherent design method which can be adopted and modified t o suit site conditions. The basic equation for the restrained strain in a slab is defined in Equation 3.2 of ClRlA 660(5) as follows:

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where:

T,

difference between the peak temperature Tp and the mean ambient temperature T,

Tz

long-term fall in temperature which takes into account the time of year at which the concrete was cast

ac

coefficient of thermal expansion of concrete autogenous shrinkage drying shrinkage restraint factor that applies during the early thermal cycle restraint factors applying to long-term temperature movement and drying shrinkage respectively coefficient for the effect of stress relaxation due to creep under sustained

E,,

E,,

R, R,, R, K,

loading (taken as 0.65) The first part of this equation represents the basic early thermal strain, which is usually based on three-day values and with restraint factor R, based on the restraint due to the adjacent slabs, walls and formwork. Values between 0.2 and 0.4 are commonly adopted. The second and third parts of the equation are long-term components of shrinkage strain. Part two expresses the strain which can occur if slab is subject to solar gain followed by rapid night cooling. For slabs which are to be enclosed, the greatest risk is likely to occur during construction and is therefore unlikely to coincide with ultimate shrinkage strains. However, special care needs to be taken with car parks and similar structures which can be exposed to temperature effects for the life of the structure. Part three of this equation relates to the ultimate shrinkage. In both of these later stages the restraint factors are different from those adopted for part one of the equation. An expLanation of these follows later in the method.

Step 1 - Minimum area of reinforcement The concept of minimum reinforcement is discussed extensively in Section 4.3 This leads to: 2

(0.8 to 1.0) fctmlfyk

This is the minimum area of reinforcement for simple direct tension. In reality there will always be a combination of flexure and direct tension, in which case AS,,,, should be adopted, see Chapter 9. The reinforcement should be distributed evenly between top and bottom faces, preferably no more unevenly than 60:40. It is not necessary to superimpose the effects of bending and direct tension. This is because once a crack forms it has done its job, and - provided the reinforcement remains elastic - further contraction strain from whatever cause will not widen the first crack but will produce another crack. The greater amount of reinforcement required for either bending or direct tension will therefore be enough to cover the other case also.

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End restrai

- L

Provided the reinforcement exceeds A5,m,n,the crack width will depend on a number of factors: 1. percentage of reinforcement 2. cover to reinforcement 3. strength of concrete 4. relative influence of flexural and direct forces 5. aggregate selection and cement class.

Thus in a typical slab the pattern and width of cracking will vary throughout the top and bottom surfaces dependent on the above factors. holes and local rigid restraints can further influence these initial crack patt f finite-element programs can give an indication of where cracking is likely t It must be remembered that most p ms treat concrete as an elastic material and the stresses shown will not be achieved, as once the tensile capacity is exceeded the forces w i11 redI s t ribut e

Step 2 - Determine the restraint factor If the slab were supported by columns of negligible stiffness there would be no restraint to movement and hence little or no stresses to cause cracking. On the other hand if a slab is attached to 100% rigid cores, the contraction is completely restrained. Between these two conditions intermediate cases can occur where the restraint factor will be less than 1. A simple chart can be established for each slab to calculate the degree of restraint (see Figure 27).

Figure 27 Approach for determining restraint factor.

Deflection of column or wall due to full restraint of free slab movement (mm)

Free shrinkage movement of slab (mm)

0

t Restraint

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The net shrinkage movement allowing for internal restraint from reinforcement is determined in Section 5.1.1 as:

The deflection of the restraint elements is determined from:

6= N h3/3Eef1 where:

h

feK I

height above the fixed base level effective modulus of elasticity of concrete, i.e. adjusted for long term effects second moment of area for the restraint; where axial compression in the restraint is low the effects o f cracking should be considered

Having calculated the restraint factor, the restrained contraction, i.e. that part of the contraction that has been prevented from occurring, can be found from: E, = RE,,

And the stress developed in the slab can be found from:

Assuming long-term shrinkage dominates, as in enclosed structures, f,,can be taken as 0.8fct,. However, in exposed structures temperature will probably dominate, and fct should be taken as 1.0 f,,. If or is greater than f,, the slab may crack, the calculated stress will n o t be realised, and the actual stress will be limited t o f,,. If U, is less than f , then the slab will behave essentially in an elastic manner. (In calculating U, i t may be necessary t o consider other locked-in stresses, see Section 1.6.)

Step 3 - Modify for local effects Modify the total force acting on a slab for the effect of the local nature of the restraint attachment together with holes and the width o f the restraining elements. In complex situations, this can be achieved by a finite-element model (see Figure 28). An initial tensile strain should be applied t o the model (this may be achieved in some software by considering an equivalent temperature drop). The strain applied will depend on the modelling of the restraint. If the restraint is rigid then a strain E, should be applied; however, if the flexibility of the restraint is modelled then E,, should be applied. Again it will generally be appropriate t o use the long-term stiffnesses of both the slab and the restraints.

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Figure 28 Stresses induced in slab by 10°C teqperatwe drop. Lighter shading represents areas of high stress.

Where the slab has been determined as uncracked due to restraint in Step 2, the stresses in the slab and the forces in the restraint can be determined directly from the finite-element model. It can be seen that the zones remote from the core are unlikely t o contribute to the slab restraint. re the slab has been determined as cracked, the slab stresses should be inspected for areas where the stress exceeds f,. In these locations the stresses should be reducedto fc,, either by hand and the revised reactions calculated manually, or by reducing the stiffness of the areas such that the stress reduces below 0.8ft,. The latter approach is more appropriate where the structure is complicated and the opportunity exists for stresses to redistribute around the slab.

Step 4 - Crack spacing If the restraints provided by the support structures are such that the stress induced in the slab does not cause cracking, it can be assumed that the slab will deform by free contraction. Alternatively, once the restraints generate forces which exceed the tensile capacity of the slab, subsequent cracking will maintain the deformed condition without further movement. In this case full restraint may be assumed and the equations for cracking in Chapter 9 apply.

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8.2.3 Frame action

Provided that each successive floor is of the same layout and slab depth, then the ultimate contraction of each slab will be the same. In simple terms this implies that a structure would shrink to the form as shown in Figures 29a and b (or intermediate between the two) and that bending is only induced in the ground-first floor columns. The effect is a reduction to the risk of shrinkage cracking in floors that are essentially the same as the floor below. Only where significant changes to layout and stiffness occur will it be necessary to recalculate the reinforcement required for shrinkage control. In reality the ground-floor restraints are unlikely to be infinitely stiff and if necessary this factor can be taken into account to reduce the tensile stress.

Figure 29 Illustration of frame deformation due to slab contraction.

a. Symmetrical stiffness

Y

A

Y

A

Y

A

I

I

A

A

A

A

A

A

A

Y

YA

A

A

A

A

I b. Asymmetrical stiffness

Y

A

8.2.4 Post-tensioning

Y A

Y

A

8

Unlike reinforced concrete, post-tensioned concrete slabs are likely to be stressed up to an average value of 1.5-2.OMPa and added to this is the tensile capacity of the concrete itself. This means that initially the slab behaves as a homogeneous elastic plate. Thus the supporting members have to deflect to suit both the initial elastic shortening and the subsequent creep and shrinkage phase.The absence of cracking in the slab means that there can be no relief from the build-up of the tensile forces until both the initial prestress and the tensile capacity are exceeded. Thus the force generated in restraining members can be as much as twice that of a reinforced concrete slab. If the level of restraint proves to be significant and/or the losses of prestress due to cable wobble and curvature are underestimated,there can be a risk of a small number of significant shrinkage cracks occurring due to the low level of bar reinforcement and wide tendon spacing.

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Alternatively unstressed reinforcement could be provided which would permit controlled cracking t o occur at more frequent intervals and thus relieve the stress. It should be noted that t o cause multiple cracking the capacity of this reinforcement (and any bonded post-tensioning crossing the initial crack) is required t o be greater than the tensile strength of the concrete plus the initial prestress.

8.3 Basement ground slabs

Basement floor slabs - which can include raft foundations - are often restrained by footings or piles and pile caps, sometimes even by friction with the soil. The application of end restraint principles t o this situation is best illustrated by a case study, see Chapter 11.

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9. Calculation of crack widths The crack width in any concrete element can be best thought of as the average strain at the surface, less the actual strain in the concrete multiplied by the crack spacing. This requires an estimation of both the average elongation/deflection, and an estimation of the tension stiffening which is needed t o estimate the strain in the concrete between cracks. On top of this, the crack spacing needs t o be estimated. Given the number of factors involved, crack width calculations should be considered a t best as reasonable estimates. In addition most crack width calculation methods make a number of approximations based on empirical data often obtained from specimens significantly smaller than real structures.

9.1 PrinCipkS

Calculation of crack widths in elements undergoing restrained movements can be separated into two cases, i.e. elements that are restrained along their edge (Chapter 7) and elements that are restrained at their ends (Chapter 8). The calculation of crack widths for the two cases is somewhat different. For elements restrained along their length the crack pattern is defined by the restraint along the edge and individual cracks are all formed early on. In this case, the crack width is related t o the restrained strain. With a slab restrained at each end, when a crack forms it opens t o its design value then, when the force in the reinforcement at the crack increases sufficiently another crack is formed. This continues with the number of cracks being related t o the total movement that has taken place. The maximum crack width is unaffected by the overall movement and thus crack width calculations that relate the crack width t o the restrained strain are flawed.

9.2 Minimum reinforcement content

All crack width theories first assume that the reinforcement is in the elastic range, i.e. that the cracks are controlled by the reinforcement; this defines the minimum reinforcement required (see Chapter 4). Chapter 7 discusses whether this minimum is strictly necessary for the edge restraint condition, however it is generally recommended that it is provided. BS EN 1992-1-1 sets the minimum steel as follows:

(BS EN 1992-1-1 Expression 7.1) where: minimum area of reinforcing steel within the tensile zone area of concrete within the tensile zone. The tensile zone is that part of the section which is calculated to be in tension just before formation of the first crack absolute value of the maximum stress permitted in the reinforcement immeU, diately before the formation of the first crack. This may be taken as the yield strength of the reinforcement, A lower value may, however, be needed t o satisfy the crack width limits according t o the maximum bar size or spacing fct,efi mean value of the tensile strength of the concrete effective at the time when the cracks can first be expected t o occur = fctm or lower (fc,, ( t ) )if cracking is expected earlier than 28 days

AS,,, Act

Sk.

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k

coefficient which allows for the effect of non-uniform self-equilibrating stresses, which lead t o a reduction of restraint forces = 1.0 for webs with h I 300mm or flanges with widths less than 300mm = 0.65 for webs with h 2 800mm or flanges with widths greater than 800mm. Intermediate values may be interpolated. It should be noted that ClRlA Report 660(5)provides slightly modified values for deeper sections coefficient which takes account of the stress distribution within the section immediately prior t o cracking and of the change of the lever arm. For pure tension kc = 1.0, and it is recommended that this value is used for all cases of restraint. BS EN 1992-1-1 provides alternative values for bending or bending combined with axial forces

kc

Depending on the consequences of cracking, Section 4.3.3 notes that it may be appropriate t o increase this area of steel by 25% for early-age effects on immature concrete.

9.3Crack Spacing

Having ensured that the minimum steel is provided, the crack width can be calculated from the crack spacing multiplied by the strain absorbed by the cracking. BS EN 1992-1-1 defines this as follows:

wk

= ’r,rnax (s‘m

- ‘crn)

(BS EN 1992-1-1 Expression 7.8)

where: sCrnax maximum crack spacing mean strain in the reinforcement under the relevant combination of loads, including the effect of imposed deformations and taking into account the effects of tension stiffening qrn mean strain in the concrete between cracks The appropriate value of ( E ~ ,- zCm)will depend on the form of restraint but the maximum crack spacing can be determined as:

Sr,rnax

= ‘3‘

+

k,k$,# 1 Pp,eff

(BS EN 1992-1-1 Expression 711)

where:

#

bar diameter

Pp,eff

As’Ac,eff

c

where: effective area of concrete in tension surrounding the reinforcement of depth hc,ef. For restraint forces where the complete section is in tension hc,ef is 2.5(h - 4, where h is the thickness of the section and d the effective depth of the reinforcement. Separate values of hc,efshould be calculated for each face cover t o the longitudinal reinforcement

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coefficient which takes account of the bond properties of the bonded reinforcement = 0.8 for high bond bars

k,

= 1.6 for

bars with an effectively plain surface (e.g. prestressing tendons) It should be noted that ClRlA 660(5)recommends increasing k, for early-age effects due t o concerns about bond. However for mature concrete, and particularly for slab-type elements where bond is likely t o be better, this is n o t considered necessary. coefficient which takes account of the distribution of strain = 1.0 for pure tension; for other cases refer t o BS EN 1992-1-1 The values of k, and k, for use in a country may be found in its National Annex; in the UK they are 3.4 and 0.425 respectively.

k,

As discussed in Section 9.1 in the edge restraint situation cracks are likely t o appear at the defined spacing and then open t o their design value, whereas cracks from end restraint will open t o their design value before another crack forms and will only achieve the design spacing once stabilised cracking is reached. Stabilised cracking is unlikely t o be achieved due t o restraint effects from normal shrinkage and thermal movements. In the end-restrained condition crack spacing is likely t o be larger than calculated, although the derived crack widths should be reasonably approximated.

9.4 Edge restraint

The value t o take for (E~,,,- EJ can be calculated from: (Esm

- E m ) = 'ax

Rax

9.5 End restraint

for edge restraint depends o n the restrained strain. This

Eiree

(BS EN 1992-3 Expression M3)

restraint factor (0 I RaxI I), which can be found from Annex L of BS EN 1992-3. For most practical situations of edge restraint a value of 0.5may be taken, in some limited locations lower values may be appropriate total free strain due t o shrinkage and thermal effects at the time considered

For a member restrained at its ends the value o f (E~,,, - EJ

can be calculated from:

where:

os

ae

k,

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stress in the tension reinforcement assuming a cracked section. For restrained cracking this can be found by replacing As,m,, with As,provin BS EN 1992-1-1 Expression 7.8 and solving ratio fjf,, factor dependent on the duration of the load = 0.6 for short-term loading = 0.4 for long-term loading

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In BS EN 1992-3 (and ClRlA C660), the above equation has been modified to: E,, - E,, = P . 5 a,

kc k fCt,df(1 + l/a,p)l/ E,

(BS EN 1992-3 Expression M I )

where: kc and k are as defined in Section 9.2

In fact if the simplification is made that:

k, = 0.5 k, k and P = Pelf then the equations can be shown t o be very similar to Expression 7.9 containing one extra term related t o the elongation of the concrete between cracks. Practically, the equations give similar results although Expression M.1 will generally yield lower crack widths in thicker sections when peffis significantly bigger than p. Both approaches are considered appropriate for calculating crack widths for conditions of end restraint.

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10. Mitigation measures For the achievement of high-quality concrete structures, design for movement cannot be left as an afterthought as it is an essential aspect of the design process.

10.1 Phlning requirements

The planning of a building t o accommodate movement must be considered at the earliest possible stage of the design process. Key decisions must be made about the degree of cracking which will be acceptable. This should either be specified by the client or the achievable design standard should be defined by the designer. Concrete structures have t o fulfil many important roles ranging from domestic t o laboratories and may include radiation protection, waterproof basements and fair-face concrete. Key decisions have to be made about whether t o provide movement joints and their location depending on the lateral stiffness of the structure and the effect of restraint. The effect that large holes in the structure might have on the flow of forces needs t o be understood. Having decided on the quality of finish and crack widths which will be acceptable, then a range of actions become possible. Some decisions will be in the control of the designer, and may require a tighter control of the specification. Other areas will be in the control of the contractor and here it might be necessary t o carry out studies t o understand the influences of strength, aggregate, blends of cement, formwork, curing, time of casting, shrinkagereducing admixtures, and size and sequence of pours.

10.2 Post-tensioned slabs

One solution that is often proposed is the use of post-tensioned concrete. In the initial stage the axial compression in the concrete can be augmented by the PIA term. This can work reasonably well when the slabs are partially restrained or restrained at one end only. Where significant restraint can occur it might be necessary t o decouple the slab t o ensure that the prestress takes full effect. For general flexural design the PIA term tends t o be small and in many cases post-tensioned slabs tend t o be constructed using high-strength concrete. In the majority of cases this is good as f,,, + P/A is unlikely t o be exceeded in a low-restraint condition. However, where significant restraint can develop there is a risk of major cracking unless the slab has sufficient + PIA is exceeded. reinforcement t o control crack widths once fCtm If post-tensioned concrete is t o be adopted solely t o control cracking, careful consideration

needs t o be given t o the degree of restraint and the provision of anti-crack reinforcement.

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10.3 Reinforced slabs

Where a structure is relatively flexible and not subject to significant restraint, early thermal shrinkage is likely to be the controlling condition. Conversely it can be see that for highrestraint conditions the long-term shrinkage is likely to be the critical case. It is recommended should be adopted consistent with that the lowest practicable concrete strength, fck, durability etc. as high-strength concrete has a higher demand for reinforcement once cracks occur. This has an important bearing on the specified strength of the concrete compared to the strength that is delivered to the site. Normally the engineer is only concerned to ensure that the only concrete has a guaranteed minimum strength.Thedesign should be based on a reasonable margin of exceedance, generally taken to be 8/10MPa, and the ASmlnshould be determined with this in mind. Consideration should be given to specifying an upper limit on strength, say fck+ 16/20MPa, where crack control is important.

10.4 Slab thickness

For a basement ground slab, the case study in Section 11.2 shows that the preferred approach is to make the slab as thin as will perform the structural function, and then provide the percentage of reinforcement that will control the cracks adequately. BS 8102 recommends a minimum thickness of 250mm for slabs and walls, and this will be sufficient. The same applies to superstructure slabs, although the requirements for controlling deflection often limit the extent to which the thickness can be reduced. To give a simple example, if a 300mm thick slab with 0.67% reinforcement is reduced to 250mm but with the same reinforcement, now 0.8%, the crack widths will reduce by 25%, demonstrating the importance of the percentage of reinforcement.

10.5 Aggregate SekCtiOn

It is not always possible or economic to specify the aggregate type, but as can be seen from

BS EN 1992-1-1,the choice of aggregate can have a significant effect on the modulus of and hence the tensile strain capacity of the concrete, E,'". In the long-term elasticity, fcm, restrained condition, the benefit of the tensile strain capacity is unlikely to be sufficient

to prevent cracking. When cracking occurs in concretes of similar strength and humidity, the variation in crack widths for a range of aggregates is in the order of 10%. For thermal movements, the choice of aggregate can be highly significant with coefficients of expansion ranging from 14pd"C for quartzite to 9pdOC for limestone.

10.6 Cements

BS EN 1992-1-1distinguishes three cement classes, namely 8, N and R, which are understood to mean Slow, Normal and Rapid hardening.A basic definition is given in clause 31.2 (6) of BS EN 1992-1-1 but, apart from this, little guidance has been provided in respect of this

important clause. As indicated in Section 2.3, it is important to note that these designations are not the same as those in the cement standard, BS EN 197(*).The Eurocode Classes are related to the cement designations as discussed in Section 2.3.

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10.7 Control Of pour Sizes

The larger the area of the pour, the greater the risk of cracking if there is significant restraint. The layout of bays and construction joints and the construction sequence should be arranged wherever possible to: have straight construct ion joints reduce the size of a pour t o a practical minimum have regularly shaped bays (ideally with a length-to-width ratio less than 2) avoid long, thin or irregularly shaped bays cast bays se q ue nt ially rather than h it-and - m iss work away from areas of greatest restraint, e.g. core areas minimise the time interval between successive (adjacent) pours for edge restraint; maximise the time interval for end restraint corners with angles less than 60" are vulnerable and wherever possible 90" or more should be provided avoid re-entrant corners and forming holes close t o the edge of the slab. Construction joints are beneficial as they are the equivalent of the first controlled crack; however, once all construction joints have opened t o form another crack the reinforcement across the construction joints must be sufficient t o act against the full tensile capacity of the concrete. This means that the designed reinforcement should be continued across construction joints. For large-area pours consisting of many deliveries of concrete, delays and variability of concrete strength throughout the slab can occur. The first crack will occur at the weakest point, not necessarily at the mid-point between two restraints. If there is a large area of sub-standard concrete, the second crack could occur close t o the first. The design of a slab t o accommodate movement derives the minimum amount of reinforcement in the cross-section. In the initial stage the reinforcement has no influence on where the cracks will occur. However, if the percentage of reinforcement is not constant along the total length of the slab, cracks that form in zones of high reinforcement content will be finer and less noticeable than those in minimum reinforcement zones. Sudden changes of reinforcement in the cross-section should be avoided. For large holes in slabs, special consideration should be given t o the increase in tension which can result as restraint forces are diverted. In many cases a crack will result and it might be preferable t o provide a construction joint in these locations. Take special care where changes in level occur.

10.8 Pour Sequence

60

Early-age contractions are a significant source of movement in concrete. However, they are complete once the concrete temperature has fallen back t o ambient, usually within seven t o ten days. The time lapse between successive pours is usually of this order (or longer), so it makes sense t o plan the pouring sequence so that the cumulative effects are minimised.

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When a pour is cast against a section of concrete which has completed its early-age cycle, it can be difficult t o understand how and where the contractions in the new concrete will occur. It can best be understood by thinking of the movement in two separate stages which are then added together using the principle of superposition:

1. Estimate the movements that will occur with the pour standing on its own unconnected t o any other structure. 2. Calculate the effect of translating the pour t o close the gap or gaps against previously cast structure.

10.9Pour strips

Another way of reducing the restraint forces is t o introduce pour strips.This allows some of the movement t o occur in the slabs before they are locked together or t o cores or shear walls. This is a valid approach but the real benefits need to be considered carefully. Early thermal effects can often be reduced significantly by sensible pour strategies without the use of pour strips. Therefore the main benefits of pour strips are in reducing the forces due to shrinkage (and creep in the case of prestressed slabs). Total shrinkage related t o time is shown in Figure 30 for a 300mm deep C32/40 slab a t 50% RH, calculated in accordance with BS EN 1992-1-1. It should be noted that actually during construction the slab will be in an external environment for some time and the initial rate of shrinkage may, therefore, be even slower. Hence it is likely that a pour strip left open for only 28 days will have completed less than 15% of its shrinkage and significantly longer periods are required to get any real benefit, this in turn may affect the construction programme.

Figure 30 Percentage shrinkage related t o time for a C32140 concrete slab 300mm thick a t 50% RH.

Shrinkage with time for slabs loo

80

s

d

60 40 20 0 1

100

10,000

Time (days)

For post-tensioned slabs the creep that occurs before the pour strip is completed also reduces subsequent restraint forces. The development of creep with time is shown for the same concrete in Figure 31. It can be seen that at 28 days about one-third of the creep has occurred. Again if the slab is in a more humid environment typical of UK construction conditions, less of the creep will have occurred. For these reasons it is usually too restrictive t o provide pour strips to relieve anything other than early-age contractions, and there is little benefit in leaving them open beyond ten days or so.

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Figure 31 Percentage creep related to time for a C32140 concrete slab 300mm thick a t 50% RH.

Creep with time for slabs 90

80 70 60 50

s 40

30 20 10

0 1

10.10 Column grids

10

100

1000 Time (days)

10,000

100,000

Special care needs to be taken with the selection of rectangular grid layouts for flat slabs, especially where the minor span and hence least reinforcement are in the same axis as the major contraction. The minor span reinforcement is usually in the second layer which in turn means extra cover and hence this could result in wider cracks.

10.11 Structural stability

Avoid the provision of rigid cores at each end of long slabs. If necessary provide movement joints to relieve the stress. Be prepared to accept large movements in the end bays of long structures and to design the columns and infill wall panels with appropriate details to deal with the expected movement.

10.12 Modified concrete mixes

Shrinkage in concrete occurs due to the loss of water.This is mostly through drying (drying shrinkage, see Section 2.3) but in very low water/cement ratio concrete the consumption of water by hydration can become significant (autogenous or hydration shrinkage Section 2.1.2). There are two main approaches to reduction of drying shrinkage:

1. reduction of free water content within the concrete mix 2. reduction of the surface tension within the pores. Reduction of free water content in a concrete mix can be achieved by the use of plasticising and superplasticising admixtures to provide the required workability and by minimisation of the cement (paste) content. The use of fly ash within the cement can help reduce water demand because of the lubricating effect of its spherical particle shape. Maximisation of coarse aggregate size can help minimise cement content through the reduction in the quantity of cement paste required.The extent to which free water content can be reduced will depend on various factors including aggregate surface texture, sand grading, cement type and fineness, and practical requirements for workability. Some low water content

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mixes can tend towards thixotropy in their rheological behaviour, particularly a t low free water/cement ratios (i.e. relatively high cement content). While it is well known that reducing the water content will reduce the drying shrinkage, quantification of the benefit is more difficult and reference should be made to specialist publications or past experience.

10.13 Curing

Water curing of slabs for a minimum of seven days or longer is most important. Curing does not reduce the ultimate shrinkage but instead allows the tensile strength of the slab If possible to develop and relaxes the surface shrinkage strains (see Altoubat and Lar~ge(~)). the use of mist sprays is an effective method for maintaining high levels of humidity. Humidity is a key factor in the reduction of shrinkage stresses.The final use and humidity level of the building can have an important bearing on the shrinkage design. In the United Kingdom, slabs cast in the winter have a slower build-up of shrinkage than those cast in the summer months. This can be advantageous as it allows appreciable build-up of strength. However it must be accepted that in the long term the ultimate shrinkage will be the same.

10.14 Cooling the concrete

In some circumstances it may be necessary to cool the concrete to reduce early thermal effects. There are various methods available for achieving a reduced concrete temperature, including reductions in the temperature of the constituents, the use of ice in the mix water and the use of liquid nitrogen to cool the concrete immediately prior to placing. Spraying the formwork with water before commencing concrete placement or commencing concreting in the late afternoon is also beneficial. The most common methods involve cooling one or all of the individual mix constituents. This can be achieved with relatively simple and cheap techniques which include the following: U

Shading the aggregate stockpiles from the direct rays of the sun or controlled sprinkling of the aggregate stockpiles. Cooling the mix water. The specific heat of water is about five times that of the aggregate and cement. In addition, water is much easier to cool and the temperature can be controlled more accurately. As it is practicable to cool water to about 2OC, this is a very effective method of cooling the concrete. Cooling the concrete using ice. Note that 1kg of melting ice is equivalent to cooling 1kg of water through about 8OoC or Ikg of aggregate through 445°C. Hence, a relatively small volume of ice can have a significant cooling effect. Ice is usually added to the mix in the form of crushed or shaved ice as it is important to avoid incorporating larger fragments of ice that melt slowly, leading to the formation of voids in the hardened concrete. Cooling the aggregate using liquid nitrogen.The method involves spraying a mist of liquid nitrogen into the mixer a t a controlled rate. This is achieved with a customised lance which is inserted into a mixer truck. As the cooling is achieved immediately prior to placing the concrete, concerns about the concrete warming up during transportation are avoided.

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0

Cooling the concrete in situ. There are two approaches: either casting a network of cooling pipes within the core of the pour or attempting to reduce the core temperature rise by surface cooling with water. Either method may be appropriate when the specification prevents the use of concrete with low heat generating characteristics. An embedded cooling system has the advantage that it can be designed to accommodate any mix type but the system must be an integral part of the design. Pumping chilled water or air through these pipes absorbs the heat of hydration of the cementitious materials and thereby reduces the temperature rise. The system must be designed to remove heat at the required rate without inducing excessive internal temperature differentials. For this reason, plastic pipes may be preferred to metal pipes as the heat flow into the coolant is limited by the conductivity of the pipe itself.

These practices to cool the fresh concrete are more commonly used in climates that are hotter than the UK. In the UK very few producers have installed the equipment needed for these techniques and, in most cases, they are unlikely to be cost-effective. However, there are situations where it may be needed technically or as a cost-effective option on a large project. In these situations, it is better to specify the maximum concrete placing temperature required (with a note reminding the producer that this is likely to require the application of special techniques) than to specify the method. One should also check the producer’s proposals for achieving the specification and make arrangements for checking the temperature of concrete a t delivery.

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11. P ract ica I applications This chapter considers various applications in which movements and the resulting cracking are particularly significant.

11.1 Basements 11.11 Introduction

113.2 Types of movement

111.3 Degree of restraint

The provision of movement joints in underground structures should be avoided wherever possible. Sometimes this is not possible, for example a basement common to buildings of significantly different height and subject to different settlements. However, generally the difficulties in detailing the joint, particularly where it is required to be waterproof, will be more severe than designing it out. Engineers are generally familiar with the design of long continuous lengths of concrete retaining wall and base slab: the design of other elements is less clear.

The various types of movement have been discussed earlier. In a reinforced concrete element with no restraint, a thermal movement will result in an overall change in length of the element with little residual stresses. Shrinkage of the concrete, however, will cause an overall shortening of the element, creating a residual compression in the reinforcement and a corresponding tension in the concrete. ClRlA Technical Note 107, Design for movement in buildings(31), provides information on the detailing of joints should they be required.

An element undergoingthermal or shrinkage movements is restrained by: the concrete it is cast against fixity a t its ends friction, where it is cast against ground. Friction is worth further consideration in that, following the logic of Deacon(32), relatively short lengths of wall or slab can be shown to be fully restrained against movement particularly where thickening such as pile caps or pad foundations exist. As the age and hence tensile strength increase, the frictional force required to restrain the shrinkage (i.e. cause the section to crack) increases. This increases the length of the element required before full fixity is reached; however, the additional weight of the building once complete will add significantly to the frictional resistance. It is difficult to calculate exact values but it is likely that the walls and slabs in the centre of many commercial building basements are fully restrained by friction. This is important as once the section is fully restrained its behaviour will be independent of further increases in the length of the structure. Providing the section is detailed correctly, the performance of a very long element of substructure without joints should be no worse than the performance of a similar fully restrained section in a much shorter element.

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111.4 Thermal and shrinkage movements

The temperature of retaining walls and base slabs will be moderated significantly by contact with the ground. At depths greater than about 4m the temperature of the soil remains sensibly constant and ‘coolth’ is radiated in through the perimeter walls and ground slab, to achieve a steady state for the life of the building. Drying shrinkage will also be reduced when there is contact with wet ground or where waterproofing systems prevent drying. Where long-term movements are expected, for both walls and ground slabs the design is controlled by the end restraint case, see Section 9.5. The longtitudinal stiffness of the retaining walls provides restraint to the shrinkage of suspended basement slabs which will tend to dry out more quickly and be subject to temperature variations. As the slab contracts, it attempts to pull in the opposite perimeter walls. Remote from return walls the perimeters walls are free to move in, indeed earth pressure may push the wall in and maintain an overall compression in the slab. However, a t return walls, including corners, the slab can prop across onto the return walls and the perimeter walls are no longer free to move. Further contraction of the slab leads to tension and possible cracking.This is shown in Figure 32.

&A Generally it is not practicable to include movement joints in basement slabs as these can conflict with the requirement to provide continuous propping or the facility for the outer perimeter slabs to act as horizontal beams in the form of an annulus. It is therefore preferable to ensure that sufficient reinforcement is available to control cracking.

11.2 Case study - basement floor slab

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Basement floor slabs - which can include raft foundations - are often restrained by footings or piles and pile caps, sometimes even by friction with the soil. A typical example is illustrated by the following case study.

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Practica I applications

Aoove reir

Figure a3

General view of a typical basement car park. Above nght

Figure 34

Close-up of cracks in Figure 33. Rlght

Figure 35

Section through floor construction of car park basement in Figure 33.

Figures 33 and 34 show the floor slab of a single-level basement 215m x 70m used for car parkingwhich has cracked extensively. The slab is 350mm thick, designed as a flat slab on pile caps at two-way centres varying between 5.5m and 6.5m. The section (Figure 35) shows that full restraintwould be a realistic assumption. Total reinforcement content p is 0.38% in the middle strips, 0.60% in the column strips, average 0.49%. Concrete strength class was specified as 28/35, although no actual cube test results were made available. The structure was built in the mid-I990s, although the cracks were only observed around 2000. They are roughly parallel, at right angles to the long dimension.They start about 27m from each end and are in groups of two to four spaced at 500 to 1100mm, roughly centred in each bay.They grew to around 0.5mm wide, and became filled with a dark grey precipitate, having leaked extensively over the three winters from 2000-2001 to 2002-2003 and been below the water table for at least part of that time. It is believed that a t the immature stage p was greater than P,,,~(see Table 7), and that controlled cracks initially formed as predicted for early-age contractions; the presenceof groups of parallel cracks is evidence for this. However, after five years and with a plentiful supply of water the concrete strength increased, p became less than p:, and with cold temperatures and shrinkage the cracks widened uncontrollably rather than addit cracks forming.

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The absence of cracks at each end probably shows the distance needed for full restraint to develop, perhaps aided by the inward pressure of the soil on the perimeter walls. The absence of cracks parallel to the long sides (and of any movement a t the construction joints, one of which can be seen in Figure 33) could be for the same reason: the width is not much more than twice 27m. However, the slab was constructed in longitudinal strips generally 5-6m wide containing only one line of columns, so an alternative explanation is that the early-age contraction cycle passed without restraint inducing any significant tensile stress, and that subsequent contractions have been within the remaining tensile strain capacity.

11.3 General observations 11.31 InCOrpOrate proprietary waterproofing admixtures?

11.3.2 Why not use tanking?

A number of products are marketed as admixtures to make concrete watertight.The

mechanism is typically that the key ingredient blocks the microcracks and pores SO making the concrete impermeable, although ‘integral crystalline waterproofing’ products claim to form crystals which block cracks up to typically 0.4mm wide. However, making the concrete itself impermeable does not stop leaks through cracks so the need to control cracks is not diminished.

In theory, an external membrane can be provided to keep the basement watertight and the concrete then be designed solely for resistance to loads. However, such membranes are expensive to apply, demand the highest quality of materials and workmanship, and can delay the construction process. Many basements are constructed within embedded pile walls, which are particularly difficult to protect in this way. More importantly, the principle is flawed, as explained in the Institution of Structural This points out that Engineers publication Design andconstruction ofdeep membranes prevent autogenous healing of early-age cracks and encourage drying shrinkage cracks. For these reasons, it is generally better to avoid tanking and instead to rely on a properly reinforced concrete structure with a drained cavity where greater assurance is required.

11.3.3 The amount O f reinforcement is too expensive?

68

When it was first published some 35 years ago, the method in BS 8007(15)took the reinforcement from around 0.2% to 0.35% - a significant increase.The approach currently promulgated (2008) increases it to over 0.6% in some situations - a further very substantial increase. However it is based on a sound theoretical approach, and is backed up by the evidence of the large numbers of newly constructed basements which still crack and leak. Furthermore,if cracking is not controlled, all the reinforcement that is in the concrete has been wasted.

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I

In the past, the approach has been to choose the concrete thickness first, usually on the basis of the thicker the better. Reinforcement has then been provided, generally as little as permitted by codes of practice. In future the approach should be the opposite.The concrete thickness should be the minimum needed to provide the required structural capacity; the minimum of 25Omm from BS 8102(17)will often be enough. Then sufficient reinforcement to control cracking should be provided (see Table 7), depending on whether the only restraint is to early-age contractions or if the mature concrete will be restrained.

11.4 Multi-storey car parks

It is important to recognise that multi-storey car parks differ in many ways from enclosed

building structures such as offices or apartments. Most importantly, they are open to the climate allyear round, and so are subject to the full range of ambient humidity and temperature.The higher humidity is beneficial, in that both shrinkage and creep (e.g.of posttensioning stresses) are less than in the lower humidity of enclosed buildings. However, the benefits stop there, as the range of temperature is far higher. Furthermore,the top deck is heated by solar radiation, made worse if it has a dark-coloured thin-layer waterproof coating (see Section 2.5.4). Evans and Clarke(34)give details of monitoring carried out on a three-storey in-situ concrete car park in the 1980s.The structure was approximately 100m x 50m in plan, divided in

two by a movement joint. Cracks had formed at a number of locations near the tops of the columns a t their junctions with the main beams supporting the top deck. Concrete temperatures and strains were recorded over a period of about 18 months. Differential temperatures of up to 15°C were recorded between the upper surface of the top deck and the soffit of the supporting beams, broadly in line with those suggested by BS 5400-2(12). It was concluded that the stresses induced a t the supports by the resulting rotations would have been sufficient to cause the observed cracks in the columns. Once cracks formed, the top of the column acted as a hinge, providing significantly less restraint than previously. Measurement of the movements across the cracks in the columns closely mirrored the changing differentialtemperatures.Similar results were reported by Williams and clement^(^^) who monitored a precast car park. Again the columns were cracked due to temperature variations through the thickness of the top deck. While in the cases reviewed above, the thermal movements did not lead to particular problems beyond cracking, this is not always the case. For example the bowing of precast planks can cause the bottom of the plank to move on its bearing; this in turn can lead to spalling of the bearing. It is therefore essential that thermal bowing is considered, and accounted for. This could be by acknowledging the formation of a hinge in the structure, by accommodating movement of the elements via slip bearings, or by ensuring that the elements are sufficiently tied to the support so that any rotation leads to distributed cracking rather than unintended sliding. When the car parks discussed above were constructed, there was no guidance on designing for thermal movements.The third edition of the Institution of Structural Engineers guide to the design of car parks(36)has a section dealing with design for movements and an appendix based on Part 2 of BS 5400 covering design for temperature effects.

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The plan dimensions are often large and movement joints are frequently needed The Institution of Structural Engineers Manualfor the design ofconcrete building structures t o Eurocode 2(37)published in September 2006 recommends that for reinforced concrete frame structures in UK conditions, movement joints at least 25mm wide should normally be provided a t approximately 50m centres both longitudinally and transversely. In the top storey with an exposed slab and for open buildings such as car parks, joints should normally be provided to give approximately 25m spacing. Where any joints are placed a t over 30m centres, the effects of movement should be included in the global analysis. It also recommends that joint spacing in exposed parapets should be approximately 12m. Stair and lift cores are usually needed a t the perimeter - the worst place for structural design. So it is usually best to ignore their contribution to stability and separate them from the deck structure with local movement joints. The stability bracing system needs to be near the centre of the plan or a t least to be symmetrical in location and stiffness. In split-level designs the ramps frequently provide the stability bracing. In the direction as used by the vehicles they can act as diagonal bracing, although paired up and down ramps are needed. Transversely, they are just sloping shear walls. If the ramps are not available for stability, it is usual to provide braced bays or shear walls on the perimeter (located centrally between ends or movement joints), or to rely on frame action for low-rise structures. Post-tensioning is becoming more common, and brings with it the additional contractions arising from both initial stressing and long-term creep. Control of the construction sequence is an important way of limiting early-age linear horizontal movements, particularly when post-tensioning is used. Pours should generally be isolated from any fixed structure such as ramps or cores for as long as possible to allow the early-age effects to pass without locking in any movements or restraints (see Section 10.9).The sequence of connected pours should be planned to minimise the movement a t the free edges; for instance, three pours should be cast in the sequence 2-1-3 not 1-2-3. If this is inconvenient, pours can be separated by 'pour strips' -gaps with discontinuous but overlapping reinforcement - left open as above.

11.5 Movement a t movement joints in finishes

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Once construction is complete, incorporating movement joints into the finishes can be considered.This usually takes place several months after the concrete has been placed SO that the expected movement can be calculated rather differently. first, all the early-age movements will have passed, so can be ignored. Second, it will be known when the pours were cast and what the ambient temperature was, so this can be used as the starting point. The season when the joint is to be installed will probably also be known, and it will usually be practicable to specify a limiting temperature range. So the actual movement a t a joint will be very much less than the structural movement calculated above.

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11.6 Axial shortening Of columns and wa[[s

Reinforced concrete columns and walls shorten owing to elastic compression, creep and shrinkage, although the effect is not significant for buildings less than about 10-15 storeys. The following should be considered: 0

0

The compressive stress is not constant but is relieved by creep; the reduced stress in the concrete is matched by a corresponding increase in the stress in the reinforcement. The load is applied incrementally over an extended period, inevitable during the construction of a multi-storey building. This also needs a spreadsheet approach.

Columns and walls in multi-storey buildings therefore shorten by different amounts and at different times.

Analysis of vertical shortening in a typical concrete-framed multi-storey building has to take account of the following: 0

0

U

0

0

0

0

Axial strain. Each increment of load causes an initial elastic strain which increases over time by creep. Shrinkage. Shrinkage starts immediately the early thermal contraction cycle has passed (it is assumed that this is too rapid to affect any supported structure), and then continues a t a decreasing rate. Construction sequence. Each new floor is cast at a level which overrides all the call this pre-installation shortening which has taken place beneath it. Fintel shortening, and the movement occurring after that point post-installation shortening. Loading sequence. After a floor is constructed,the remaining load is added incrementally, usually in the following sequence: screed or raised floor; walls and partitions; ceilings with lighting and other services; furniture and occupants. Time-dependent effects. The overriding problem is that creep and shrinkage are both very much dependent on the age of the concrete, and with each storey cast a t a different time the total shortening a t any one time is the sum of movements which all started a t different times and have progressed to different stages. Differential shortening. Generally it is the differential shortening between neighbouring columns and walls that is important, particularly between columns, which are generally heavily loaded, and core walls, which are usually more lightly loaded. Cores are often constructed ahead of the frame, in which case their shortening will be out of phase with that of the surrounding columns. Shortening in a single-storey height is important for added elements which are not flexible. In particular, cladding must be detailed to allow for the movement, the worst case being clay brickwork which expands. Allowances should also be made for temperature movement.

The modern answer to dealing with these issues is a spreadsheet. It is not difficult to set up a spreadsheet to represent the actions described above, but it is difficult to keep it to a manageable size and to get it to produce the information needed for design.

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Elastic and creep strains The initial elastic strain from vertical load depends primarily on the proportions of the section, although the €-value of the concrete increases with age. The creep strain depends mainly on: the age a t loading; the humidity of the environment; the composition of the concrete; and the thickness of the section. The effect of creep is to shed stress from the concrete onto the reinforcement.This effect is termed relaxation in textbooks, which go to considerable lengths to model it mathematically, usually incomprehensibly if not actually incorrectly. Using a spreadsheet which divides the process into a minimum of four to five steps is a better way. The principle of superposition means that the creep arising from individual applications of load (and the shrinkage) can all be considered separately as if no other actions were taking place and the resulting movements can then be added together. It is acceptable to group the structure into units of several storeys each effectively constructed a t the midtime, and similarly to simplify the loading into the three main steps of self-weight, finishes and occupation.

5hrinkage As shrinkage progresses, restraint of the reinforcement creates internal stresses: tension

in the concrete, compression in the steel. As described above, the stress in the concrete is gradually relieved by creep. In the spreadsheet each step of shrinkage is applied at the midtime to a structure whose properties are derived for that same point in time. Alternatively, the final movement can be approximated by applying the total free shrinkage in one step at age 150 days.

Controlling shortening Can anything be done to control shortening? In designing a reinforced concrete column or wall, the two main choices are the strength of the concrete and the percentage of reinforcement. To show how these decisions affect the amount of shortening, a simple example is presented in Section A I in Appendix A. The following tentative conclusions can be drawn from the study:

U

U U

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Maximum shortening of 1.4mm/m is possible, i.e. 4-5mm in a typical storey height. The higher the concrete area, the less the shortening; this is because the stiffness-tostrength ratio of concrete is higher than that of steel. Reducing the section size by increasing the reinforcement from 0.5% to 6% increases the shortening by 11-20%. Reducing the section size by increasingthe concrete strength from 40 to 85MPa increases the shortening by 2-11%. The shortening of two columns of the same size but different concrete strengths and reinforcement contents differs by less than 10%. The wall section shortens 15% less than the comparable column. Deliberately over-designing the section by 25% reduces the shortening by only 17%. The concrete stress in highly reinforced sections reduces by as much as 50% (35% creep plus 15% shrinkage) in the long term.

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Better control is achieved where the initial elastic shortening is a higher proportion of the total; this can be achieved by increasing the reinforcement content. The amount of shortening occurring after 500 days is the opposite way round from the total amount, i.e. higher-strength concrete and more reinforcement both reduce the late shortening. The overall conclusion is that it is difficult to reduce the shortening significantly. A better strategy is to limit the differential shortening by designing all columns to the same criteria, and by keeping long clear spans between different structural types, i.e. between interior columns and cores and shear walls on the one hand and perimeter columns on the other.

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References and further readinp

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1 BRITISH STANDARDS INSTITUTION, BS EN 1992.Eurocode2, Designofconcretestructures, Part 1-1,

General rules andrulesforbuildings, Part 1-2, Generalrules - Structuralfire design, Part 3: liquid retaining and containmentstructures, BSI, London, Various dates. 2 CAMPBELL-ALLEN, D. The reduction ofcracking in concrete, University of Sydney and Cement and

Concrete Association of Australia, Sydney, 1979.

3 CONCRETE SOCIETY. Non-structuralcracks in concrete, Technical Report 22, The Concrete Society, Camberley, 1982. 4 CONCRETE SOCIETY. The relevance ofcracking in concrete to corrosion ofreinforcement, Technical

Report 44, The Concrete Society, Carnberley, 1995.

5 BAMFORTH, P. Early-age thermal crack control in concrete. Publication C660. CIRIA, London, 2007. 6 GOODCHILD C. Design guidance on large area pours for suspended slabs, Concrete, Vol. 38, No. 6,

June 2004, pp. 19-22.

7 ALTOUBAT, SA and LANCE, DA. Creep, shrinkage and cracking of restrained concrete a t early age, ACI Materialslournal,July-August 2001, pp. 323-331. 8 BRITISH STANDARDS INSTITUTION,BS EN 197. Cement, Part 1, Composition, specification and

conformity criteria for common cements, Part 2, Conformity evaluation, BSI, London, 2000. 9 BOND, AJ et al. How to design concrete structures using Eurocode 2, The Concrete Centre,Camberley,

2006. 10 BRITISH STANDARDS INSTITUTION, BS 8110. Structuraluseofconcrete, Part 1, Codeofpracticefor

design andconstruction, Part 2, Code ofpracticeforspecial circumstances, BSI, London, 1997 and 1985. 11 CONCRETE SOCIETY. lnfluence oftension stlffening on deflection ofreinforced concrete structures,

Technical Report 59, The Concrete Society, Carnberley, 2004. 12 BRITISH STANDARDS INSTITUTION, BS 5400. Steel, concreteandcomposite bridges, Part 2, Specification ofloads, Part 4, Code ofpractice for design ofconcrete bridges, BSI, London, 2006 and 1990. 13 BRITISH STANDARDS INSTITUTION, BS EN 1991. Eurocode 7:Actionsonstructures-Generalactions,

Part 1-5, Thermalactions, and UK National Annex, BSI, London, 2003. 14 BUILDI NC RESEARCH ESTABLISHMENT. Estimationof thermal and moisture movements in

structures, Digest 228, BRE, Carston, Watford, 1979. 15 B R IT1S H STANDARDS INSTlTUTlON, BS 8007. Design of concrete structuresfor retaining aqueous

liquids, BSI, London, 1987. 16 HUCHES, BP. A new look a t rigid concrete pavement design, Proceedings ofthe lnstitution ofcivil

Engineers.Transport, Vol. 156, No. 1, February 2005, pp. 29-36. 17 BRITISH STANDARDS INSTITUTION,BS 8102. Code ofpracticeforprotection ofstructures against waterfrom theground, BSI, London, 1990. 18 CONCRETE SOCIETY. Self-compacting concrete: a review, Technical Report 62, The Concrete

Society, Carnberley, 2005. 19 ALEXANDER, SJ. Understandingshrinkage and its effects, Part 1, Concrete, Vol. 36, No. 9, October

2002, pp. 61-63, Part 2, Concrete, Vol. 36, No. 10, November/December 2002, pp. 38-41. 20 DAVIDSON, B and OWENS, CW. Steel designers’manual,Steel Construction Institute,Ascot, 2005. 21 BRITISH STANDARDS INSTITUTION,BS EN 1994.Eurocode 4. Designofcompositesteeland concretestructures. Part 1-1, General rulesandrulesforbuildings, BSI, London 2004. 22 CONCRETE SOCIETY. Crackingin composite slabs, Concrete Advice Sheet 13, the Concrete Society, Carnberley, 2006. 23 A t RAWI, R. and KHEDER, CF. Control of cracking due to volume change in base restrained concrete members,ACI Structuresjournal, July-August 1990.

Licensed copy: [email protected], Severn Trent Water Ltd, 11/07/2008, Uncontrolled Copy, ®The Concrete

24 STOFFERS, H. Cracking due to shrinkage and temperature variation in walls, Heron, Vol. 23, No. 3,

Delft, 1978. 25 BEEBY,AW. and FORTH,JP. Control of cracking in walls restrained along their base against early thermal movements, Concretefor Transportationlnfrastructure (Dhir, RK, McCarthy, MJand Caliskan, S,Eds.),Thomas Telford, London, 2005, pp. 123-132. 26 BEEBY, AW and SCOTT, RH. lnsights into the cracking and tension stiffening behaviour ofreinforced

concrete tension members revealedby computer modelling, Magazine of Concrete Research, Vol. 56, No. 3, April 2004, pp. 179-190. 27 HUGHES, BP. Contra/ ofthermal andshrinkage cracking in restrainedreinforcedconcrete walls,

Technical Note 21, Construction Industry Research and Information Association, London, 1971

28 BAMFORTH, PB. Concretingdeep liftsandlarge volumepours Report 135, Construction Industry Research and Information Association. London, 1995. 29 REINFORCED CONCRETE COUNCIL. Large area pours for suspended slabs: a design guide, Reinforcing

Links, Issue 3,1993 (availablefrom www.concretecentre.com). 30 BRITISH STANDARDS INSTITUTION, PD 6687. Backgroundpapertothe UKNationalAnnexesto BSEN 1992-1, BSI, London, 2006. 31 ALEXANDER SJ and LAWSON RM. Designfor movement in buildings, Technical Note 107,

Construction Industry Research and Information Association, London, 1981. 32 DEACON, RC. Concretegroundfloors their design, construction andfinish, Cement and Concrete

Association (now British Cement Association), Camberley, 1987. 33 INSTITUTIONOF STRUCTURAL ENGINEERS. Design andconstruction ofdeep basements including

cutandcover tunnels, The Institution, London 2004. 34 EVANS, DJand CLARKE,JL.Thermal movementsin a multi-storeycarpark, Technical Report 563,

Cement and Concrete Association (now British Cement Association), Camberley, 1986. 35 WILLIAMS, A and CLEMENTS, SW. Thermalmovementsinthe upperfloorofa multi-storey carpark, Technical Report 539, Cement and Concrete Association (now British Cement Association),

Camberley, 1980. 36 INSTITUTIONOF STRUCTURAL ENGINEERS. Design recommendationsfor multi-storeyandunder-

groundcarparks (Third Edition), The Institution, London, 2002. 37 INSTITUTIONOF STRUCTURAL ENGINEERS.Manualfor the design ofconcrete buildingstructures to Eurocode 2, The Institution, London, 2006. 38 FINTEL, M, GHOSH, SK and IYENGAR, H. Columnshortening in tallstructures-predictionand compensation, Portland Cement Association, Skokie, Illinois, USA, 1987. 39 BRITISH STANDARDS INSTITUTION,BS 6399-1. Loadingforbuildings. Part 1: Code ofpracticefor

deadandimposedloads, BSI, London, 1996. 40 CONCRETE SOCIETY. Designguidanceforhighstrength concrete, Technical Report 49, The Concrete Society, Camberley, 1998. 41 LAWSON, RM. Design ofcompositeslabsandbeams with steel decking, Publication 055, Steel

Construction Institute, Ascot, 1989.

Further reading

0 ALEXANDER, S.Contraction of in-situ concrete toppings, Part 1: Concrete, Vol. 40, No. 4, May 2006, pp. 45-46, Part 2: Concrete, Vol. 40, No. 5, June 2006, pp. 28-29.

0 ALEXANDER, SJ. Axial shortening of concrete columns and walls, Concrete,Vol. 35, No. 3, March 2001, pp. 36-38.

0 ALEXANDER, SJ. Why does our concrete still crack and leak?, The StructuralEngineer,Vol. 84, No. 23/24,5 December 2006, pp. 40-43.

0 AMERICAN CONCRETE INSTITUTE.ACI209R. Predictionofcreep, shrinkageandtemperature effects in concretestructures, ACI, Farmington Hills, Michigan, USA, 1992 (reapproved 1997).

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BEEBY, AW and SCOTT, RH. Cracking and deformation of axially reinforced members subject to pure tension, Magazine ofConcrete Research,Vol. 57, No. 10, December 2005, pp. 611-621.

U CONCRETE SOCIETY. The relevance of cracking in concrete to corrosion ofreinforcement, Technical Report 44, The Concrete Society, Camberley, 1995.

0 CONCRETE SOCIETY. Deflections in concreteslabsandbeams,Technical Report 58, The Concrete Society, Camberley, 2005.

0 FORTH, JP and BROOKS, JJ. Movement in a seven storey reinforced concrete frame, Proceedingsof the institution ofCivilEngineers, StructuresandBuildings, No. 156, Paper 12831, Issue SB2, May 2003, pp. 131-139. CILBERT, RI. Time effects in concrete structures, Elsevier, 1988.

0 CILBERT, RI. Shrinkage cracking in fully restrained members,ACI Structuraljournal,Vol. 89, No. 2, March-April1992, pp. 141-149.

U CILBERT, R.I. Time-dependent deflection and cracking of reinforced concrete flat slabs. In Code Provisionsfor Deflection Control in Concrete Structures (Nawy, EC and Scanlon, A, Eds.), Special Publication SP 203, ACI, Farmington Hills, Michigan, USA, 2001, pp. 157-178.

0 CILBERT, R.I. Time-dependent cracking and crack control in reinforced concrete structures. In ServiceabilityofConcrete (Barth, F, Ed), Special Publication SP225, ACI, Farmington Hills, Michigan, USA, 2005, pp. 223-240.

U CILBERT, RI and CUO, XH.Time dependent deflection and deformation of reinforced concrete flat slabs - an experimental study, AQStructuraljournal, Vol. 102, No. 3, May-June2005, pp. 363-373.

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